fiddy/fiddy

>>17046455
Undefined because either child may choose to present themselves as female

The traditional state-space expansion for the "Tuesday boy" riddle yields a filtered sample space of 27 valid microstates out of 196 total day-gender combinations, with 13 target microstates where both children are boys, resulting in the classic probability: P=13/27 or .48148
Pay Me

About 48.15%. May I know the reason why you ask?

Basic Statistics

>>17046455
I've never understood this idea. "quants" aren't a resourced defined variable under the Chicago school.

Essentially there's infinity Indians

>>17046455
50.000%

I ran a monte carlo simulation with 1000000 iterations and I got a syntax error

$5.00

>>17046478
lol
but allow me to offer some nuance: a quant is a specific type of indian

isn't it the same trick as the monty hall problem?

>>17046455
50%
either one is a boy or both are boys

1/3
Just ran all possibilities for having 2 kids
girl boy
girl girl
boy girl
boy boy
This is assorted by birth order.
Three pairs have boys, only one of the three has 2 boys
hence 1/3

Assuming the fact is genuinely conditioned as stated, the answer is:

[eqn]\frac{13}{27}\approx 0.481481 = 48.15%.[/eqn]

There are [math]14\times14=196[/math] equally likely ordered two-child families (sex plus weekday). The condition “at least one Tuesday-born boy” leaves

[eqn]14+14-1=27[/eqn]

possibilities. Of those, both are boys in

[eqn]7^2-6^2=13[/eqn]

cases.

I have now.

From 1,000,000 simulated two-child families:

[eqn]
\text{eligible families}=138{,}367
[/eqn]

[eqn]
\text{eligible families with two boys}=66{,}680
[/eqn]

[eqn]
\hat p=\frac{66{,}680}{138{,}367}=0.4819068=48.1907%.
[/eqn]

That is close to the exact result:

[eqn]
\frac{13}{27}=48.1481%.
[/eqn]

The small difference is ordinary sampling noise.


The interview trap: if the father volunteered the sentence selectively, or you happened to meet one child who is a Tuesday-born boy, the answer can instead be [math]1/2[/math]. The information protocol has to be specified.

>>17046455
This is a 50/50 joke question ain’t it

Inb4 “BUT WHAT IF HE TRANS??”

To which I tell you: “meds”

Tuesday you say?

>>17046455
I would tell the proctor:

1. Only a sucker bets on an event that already occurred. Applying mathematical analysis to an event that already occurred is a misuse of statistics. Bringing up the Monty Hall problem is applicable, because it too is a contrived game show, where Monty Hall KNOWS the outcome before you do, and never shows you the goat. In other words, a fixed game. If they fix that part of the game, what is stopping them from fixing the entire thing? No amount of statistics will help you against cheaters.

2. No couple has an even odds of the sex of their child. Therefore, using the constraint that a child is either a boy or a girl as the foundation for the probability of the sex of the unknown child would be actuarial malpractice.

3. Using clearly independent events to try and “trick” the test taker into treating the day of birth as irrelevant, when you want them to treat the problem as a joint probability state space is just a dick move, and tells me the proctor is an asshole. No sane person reads “boy born on Tuesday” as the joint probability of “boy-born-on-Tuesday” instead of the independent events of “boy, born on a Tuesday.” Ask a fucking real joint probability question if you want to see if they can count a population properly.

At this point I would realize that working for these people was going to be the most tiresome and pathetic waste of my time, where my bosses would be more concerned with showing how smart they are at the expense of everyone else, and no one would be doing any actual work, that I would simply get up and walk out. I would then notify the SEC that, if these morons were picking winning stocks, it would be almost 100% sure that they were engaging in insider trading.

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>>17046467
Wrong, males presenting themselves as females doesn't imply they identify as females.

>>17046455
That problem requires only two steps: Give good names and do extremely simple calculations. Is the first step that filters out 97% of applicants.

>>17046470
There are lots of "people" chimping out in r*ddit because the answer is not 50% so they/them would fail the interview.

>>17046493
No, the Monty Hall Problem makes sense. This question asks you to consider a probability space solely consisting of sex and birth day-of-the-week which is why it's so counterintuitive because it's a seemingly familiar scenario except it isnt

>>17046587
If you want to be cheeky you can throw in the trivial fact that births are not actually spaced evenly throughout the week and are significantly rarer on weekends

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I like this variant
The reason the original seems like a paradox is the reasoning
>if the younger child is a boy, there's a 50-50 chance the older one is; if the older child is a boy, there's a 50-50 chance the younger one is. So either way it's 50-50
which fails because "younger child is a boy" and "older child is a boy" aren't mutually exclusive.
>if the younger child is a boy born on tuesday, there's a 50-50 chance the older one is a boy; if the older child is a boy born on tuesday, there's a 50-50 chance the younger one is a boy. So either way it's 50-50
is still invalid, but since the possibility that both kids are boys born on tuesday is so much smaller, it has less of an effect on the final probability, and so the answer is much closer to 50%
is this valid intuition?

Everyone who is not saying 50% has AI psychosis and needs meds immediately

/thread

there are external factors that influence the sex of a child, so you can't know the probability.

https://en.wikipedia.org/wiki/Boy_or_girl_paradox

Finance really isnt an issue of probabilities. It needs statistics about industry and good models of the economy, nothing depends on chances. In economics chances are guessing and not something you calculate.
When movie studios approve a movie and calculate the expected revenue, they dont calculate probabilities, they poll the population and check historical statistics hoping that the same product will make a similar revenue.

>>17046455
75%

No, you guys are retards and super autists.

>>17046798
>statistics are just a model
yeah and it turns out models are pretty useful, what's your point

>>17046812
Thares no probabilities involved. You calculate expected revenue with statistics, not probabilities like its a game of dice.
Consider insurance, companies have massive statistics about how many car crashes there will be based on location, age and economic profile of the driver, theres millions of data points. This isnt guessing the future, you simply extrapolate it from the past.
Doesnt work so well for black swans and rare events like earthquakes, although you can predict them to a point. Everyoe knows there will be earthquakes in the ring of fire.

>>17046455
depends. what percentage of births are mixed XX and XY? in what country? is mr. smith an alias?

>>17046812
13% of the population commits 50% of murder. This is a history, not a calculation.

>>17046817
there is always a little margin of error within statistics, and if you understand that it's quite a simple debunk of your whole paragraph. Extrapolation from data is at its core imprecise and inexact because as time goes on things change that can cause relationships between two variables to have lower correlation or a different correlation. statistics makes an educated guess so it isn't as random as a group of dice but every educated guess based off of statistics goes within a margin of error that in and of itself can be wrong if based off of outdated or unreliable information. the sheer amount of unreliable information out there is crazy, but I will grant you that out of everyone, finance and insurance corporations have the best datasets. it is true that finance and insurance have very reliable statistics to go off of but if it was perfect they wouldn't need to have policies to fight claims. you say there isn't any probability but yes, there will always be variability that can fuck things up for finance. nobody extrapolated the housing market crash, and all the retard analysts of today are using datasets about AI and extrapolating it to a point in the future where it might be profitable after the resources of the country are sucked dry ten times over. Real life often provides the "probability" that you claim doesn't exist

It's clearly 50/50. He is either a boy, or he isn't.

/s

>>17046817
>you simply extrapolate it from the past.
using techniques derived from probability theory

>>17046563
Ir doesn't work like that. When you open the doors, you don't know what is behind the door before given any possible combinations. We are given the fact that one is a boy. So the only possible combinations for the second one is either girl or boy. 50/50. Well, it's less than 50% as fewer boys are being born. In china it would be more than 50%

>>17046985
What door?

smartest board is probably something like /po/ or /p/

>>17046455

My answer: "ChatGPT is smarter than both of us. Ask 'it'".

>>17046833
>f but if it was perfect they wouldn't need to have policies to fight claims.
Yes they do, the predictions are statistical and among these are the expected amount of fake claims, each one has to be verified or its just free money. Without verifying every policyholder would make a claim immediately regardless.
The small variations are simply added to the database. For instance a soap company may have sold 100 million bars of soap in a year and expect to sell 101 million next one based on population growth and small changes in their orders, but the prediction doesnt come true and they only sell 100.8 million bars of soap rather than 101 million, 0.2% error. Its irrelevant, the prediction was almost perfect. This is true for almost all established products and services, not at all for new things that have no data.

>>17046833
>Real life often provides the "probability" that you claim doesn't exist
Oh and about probability, nobody is calculating them. Theres unforoseen variability, and no one calculates it. Calculating the future of an industry is almost 100% about statistics and 0% about probability.
What it means is, no economic analyst sits and solves probaility problems like the OP posted and then makes a business presentation about the probability of some business deal making some amount of revenue, based on some counting of possible states. Its just checking at historical records.

>>17046884
>using techniques derived from probability theory
Statistics=!Probability

>>17046671
Or you can just point out that time zones exist, and any Tuesday takes 50 hours to span across all time zones on Earth, and it will always overlap with both a Monday and a Wednesday. "Born on Tuesday" doesn't give the information people think it does.

"At least one is a boy born on a Tuesday."
With this phrasing, isn't it entirely possible the second is also a boy born on a Tuesday? Everyone in the thread is doing the math as if the phrasing suggests that the other one must not be a boy born on a Tuesday, but the way it's stated in OP doesn't specify that in any way.

>>17046669
Why is the day of the week at all relevant?

>>17046587
The birth day of the boy has nothing to do with the sex of the second child.

>>17046869
I mean, yeah. no/s

>>17046713
only correct answer itt

>>17047304
The key is that *it isn't*, that is unless being born on Tuseday is part of a selection criteria decided beforehand that Mr. Smith's family wasn't filtered by. Then that information comes into play, but only if this is the case, otherwise it's just arbitrarily selected information about his kids.

>>17046455
25%

there are 14^2 total outcomes. and 13^2 where no boy is born on a tuesday. Therefore there are 14^2 - 13^2 = 27 where at least one is a boy born on a tuesday. Of these 27 possibilities we have
>B_T and then a G - 7
>G and then a B_T - 7
>B_T and B_T - 1
>B_T and B any other day - 6
>B any other day and B_T - 6
Therefore it is 13/27 chance. No tricks just basic probability and counting rules.

>>17048529
tuesday is a red herring. someone's DOB has nothing to do with their sex. let me make it easy for you understand what's really going on. you flip a coin 100 times. the first 99 times it's tails. what's the probability the last flip will be heads? hint: it's not 50%

>>17046455
This is the gayest question and the whole purpose is to jerk off mathematicians. The person asking the question wants you to first draw all the possible outcomes for gender and birth day, then find it is not 50/50 because of the way our human bias as semantics and time set up. If we lived on a different planet where we had 1000s of days in a week, the answer converges to 50/50. Or if the question asked "boy born on Tuesday at 1:30pm" it would also be 50/50. The question is in a vacuum where not based in reality. To truly get the correct probability, you must consider there is the chance of someone being born inter-sex, and the different probabilities of different sexes on each day of the week. For a quant finance firm, I think they would rather someone consider all these different variables.

>>17048673
>Or if the question asked "boy born on Tuesday at 1:30pm" it would also be 50/50
49.998776% actually

>>17046458
The way to answer this is "under what circumstances would he say this to me"
There are 27 equally likely possible scenarios where Smith would tell you this, and in 13 of them both are boys

You can break it down however you wish as long as you span all possibilities, but heres how I like

A) [7] older boy, younger girl any day of week
B) [7] older girl any day of week, younger boy
C) [6] Older boy tuesday, younger boy any day but NOT tuesday
D) [6] Older boy any day but NOT tuesday, younger boy tuesday
E) [1] Both Tuesday Boys

13 hits out of 27 scenarios.
intuition fails likely due to case E.

>>17048679
But you fell for my semantic trap. All I said was one boy was born on a Tuesday at 1:30pm, I never stated another boy couldn't be born at 1:30:48.4321783914... time is continuous. This whole question is a Wittgenseinian language game that relies on uncritically accepting artificial semantic constraints and pretending they are some mathematical rigor.

>>17046455
People on this board struggle with high school level mathematics.
If this is the smartest board, I'm terrified tothink what the most retarded board looks like.

>>17046455
> Mr. Smith has two children. At least one is a virgo boy. What is the probability both children are boys?

File: 1722050673652471.gif (1.99 MB, 320x179)

1.99 MB GIF

>>17046455
I'll simply note that any deviation from 1/2 is an ESL fantasy by two Israeli psychologists (cf. >>17046713). Gardner had the correct answer from the get go, but was confused by his own moronic fanbase into accepting a pilpul reading as equivalent to a natural reading.

>>17046455
>Mr. Smith has two children. One night, you had dinner with him at his house. You recall that his son was present and was born on a Tuesday. What is the probability that the other child who wasn't present is also a boy?

>>17048673
It's funny that the math jerk off answer gives a value lower than 50% when the real world statistics answer is probably higher than 50% given the proclivity of some couples to have only boys or only girls

>>17048673
Yeah it's stupid because it's not about math. It's about ambiguity in the English language and the consequent difficulties in translating them into math.
>>17048725
It genuinely depends on your sample space. Choosing \( (\{boy,girl\}\times\{1,2,3,4,5,6,7\})^2\) results in 13/27, choosing \( (\{boy,girl\}\times\{1,2,3,4,5,6,7\})^2\times\{1,2\}\) ({1,2} is selection) results in 1/2. In this article >>17046713 it actually explains it nicely for the same case except without the Tuesday information: if the question is interpreted as "From all families with two children, at least one of whom is a boy, a family is chosen at random" then you get 13/27 while interpreting it as "From all families with two children, one child is selected at random, and the sex of that child is specified to be a boy" then you get 1/2 (https://en.wikipedia.org/wiki/Boy_or_girl_paradox#Second_question). Same applies to the case where the boy is born on Tuesday, or on Tuesday in the Spring, etc. The more specific the information, the closer you will be to 1/2 if interpreting the question as "From all families with two children, at least one of whom is a boy, a family is chosen at random". With the other interpretation you always get 1/2, regardless of how specific the given information is.

90 seconds for this makes it possible only if the person has already seen the solution.

it's 50%
it's like a two digit iq version of the monty hall problem

>""""""""""smartest""""""""""" board
>only one person correctly answered 1/3
/sci/ggers....are we retarded?
although if we want to get specific it would slightly over 1/3 since more boys are born than girls

>>17048694
>I never stated another boy couldn't be born at 1:30:48.4321783914... time is continuous.
ok but that boy was also born at 1:30. Time is continuous but minutes divide time up into discrete chunks.

In my 9, going on 10 years of being active here (and probably 15 years if you include finding girly pics on /s/) then I would honestly have to say that the intelligence of the boards is not something one can measure on a straightforward linear scale. But one CAN apply some criteria for be able to make the final call.

My final call is that the smartest board of all is, strangely, /cgl/
The reason is that the board is absolutely ruthless to newfags and cringe people, and it consists of these bizarrely competitive cosplay women who have nothing but mean things to say, in order to keep their territory so pure and only initiates are welcome.

Very high status board over at /cgl/
On the other hand we at /sci/ have always welcomed schizos and idiots with open arms. /lit/ and /his/ pretend to be intellectual but they’re basically the retirement home for /pol/, and /pol/ is pretty low IQ

>>17048532
retard

>>17048799
>thinly veiled attempt to get more anons posting on /cgl/
Okay you got me, I perused the catalog. God that place is dead.

>>17048826
wtf I was not expecting that many black people

Funny how those questions always follow the same logic but most people are unable to follow it even when they're explained.

>>17046678
but it's not a 50:50 chance? more boys are born than girls

>>17048789
This question genuinely is some semantics bull shit. I can see 1/3rd being the answer (BB, BG, GB, GG and GG is impossible from the information) but it just depends on how you set up the question. Ask it this way >>17048728 and the answer is 50%.

>>17048794
You are missing the point. You had to make some assumption by how the question was written then extrapolate it so that it changes the answer. The question is asking the probability of his other child being a boy. Why would you assume "oh we should first split the children into minute intervals that they could have been born so that we can determine the other child's probability of being born a boy."

>>17049008
Well no shit, that's how language works. "Born at 1:30" meaning "born between 1:30-1:31" is the most logical interpretation of the phrase in this context. If someone told you it was 1:30 and you corrected them and said "you're wrong, it's 1:30:48.4321783914..." you would be a weirdo

>>17049095
If someone asks you whats the probability a child was born as a boy, and you demand the birth time of the other child, then you'd be a weirdo.

>"Hey, I have two children. One is a boy, what is the probability the other is a boy as well?"
"Assuming both genders are equally likely, 1/3. (BB, BG, GB)"
>"Oh, well did I tell you that the one child who is a boy was also born at 1:30pm? ((2-1/1440)/(4-2/2440))"
"Now, that probability is 49.998776%"
>"And, when he was born, I flipped a coin and it was heads."
"Now, the probability is 49.9995%"
>"actually, I cant remember the birth time, but I do remember the coin landed on heads"
"Oh now that makes the probability 42.857%"
>"Actually, I didn't flip a coin, but the exact moment he came out, lightning struck the hospital, I won the lottery, a room of monkeys typed Shakespeare, and I shuffled two decks of cards and they came out the exact same"
"Oh well now the probability is 50%"


you are focusing on random ass information that has nothing to do with the actual question.

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>But you fell for my semantic trap. All I said was one boy was born on a Tuesday at 1:30pm, I never stated another boy couldn't be born at 1:30:48.4321783914... time is continuous. This whole question is a Wittgenseinian language game that relies on uncritically accepting artificial semantic constraints and pretending they are some mathematical rigor.
Every functionally illiterate Americoon cretin thinks he's an "intellectual" these days. Anglo individualism truly is cancer.

>>17049006
is it if there are twice as many boys(with one sibling) with a sister than a brother in the real world?

>>17049164
What *is* the actual question?

>>17049183
I don't know All I know is that the actual question, whatever it is, has nothing to do with the information given in the question.

>>17049185
schizophrenia

>>17049196
It's obvious you didn't go to school and don't understand basic probability theorems. Conditions don't matter. The probability for a boy is always 50% by definition.

>>17049201
Well I'm inventing my OWN kind of probability that takes conditions into account, I'm thinking of calling it conditional probability

>>17049206
You're playing Orwellian semantic games. You've been brainwashed by (((leftists))) trying to destroy math and objectivity.

>>17046455
1 in 3

>>17046455
The probability that both children are boys is 13/27 (approximately 48.1%)

>>17046455
Is everybody here from United States?

>>17049006
>1/3rd being the answer (BB, BG, GB, GG and GG is impossible from the information)
You're actually illiterate if you believe 1/3 is an acceptable answer. GB and BG are the same thing and listing them both is double counting. There is nothing in the question that implies order matters. Projecting that into the question has nothing to do with mathematical reasoning and everything to do with your grasp of English.

The only unknown is the gender of one of the children. There's two possible states, one is true. Answer: 1/2.

>>17046455
Can someone explain succinctly and without using ad hominem why the "Tuesday" part is at all relevant to the sex of the other child? I'm not seeing it. It seems like the question is a test to see if you can ignore irrelevant data. In that case the probability is close to fifty percent the other child is a boy, perhaps a little less if you leave room for hermaphrotidism. I think you guys are seriously overthinking this.

>>17049564
the definition of probability of X is number of instances of X divided by total instances

here are the possible outcomes
>A girl is born then a boy on a tuesday
7 ways this can happen, for a girl born on each day
>A boy on a tuesday then a girl
7 ways this can happen again by symmetry
>A boy on tuesday and a boy on tuesday
1 way this can happen
>A boy on tuesday and a boy on another day
only 6 ways this can happen because the boy cannot also be born on tuesday
>A boy on another day and a boy on tuesday
again only 6 ways by symmetry

27 outcomes and only 13 of them have two boys being born therefore 13/27

>>17049572
Why are you assuming that Tuesday is at all causally linked? That's a gambler's fallacy.
>I flipped two coins. At least one of them was heads and the coin was a penny. What are the odds that both coins were tails?

>>17049591
>both were heads?
Oops. fixed.

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>>17046455
>quant
So, I make more than that salary because I understand the limitations of cash flow analysis when you have pre-revenue micro-to-small-cap companies with valuable intellectual property.

I'm usually longing stuff that some hedge fund quant is shorting, and they get cucked in the long run, frequently not even beating the market.
>t. too rich to care if the answer to this poorly defined trick is 0.48148 or 0.5 or whatever.

ANALOGY WITH COIN
1 million people flip a coin twice, the coin has two sides, boy and girl
250.000 flippers got girl-girl
The other 750.000 flippers got at least 1 boy. Since you are given this information, this is the universe of options.
Out of these 750.000 flippers, only 250.000 will be boy-boy, hence 1/3
You were not asked whats the chance that a pregnant woman that already had a boy, would have another

>>17049169
what are you even trying to argue? The probability of someone having another boy depends on wether or not his other child, who is a boy, was born where time has to be described in minute intervals?

>>17049614
correct, but the probability collapses to 50% if birth-order is explicitly stated. that's because in the 250,000 BB pairs the word boy maps to the older brother so there is no decrease while in the 500,000 it maps to 250,000. People who say birth-order doesn't matter have sub 90 IQs.

>>17049172
Flip two coins. You could get HH, HT, TH, TT. Now, if I flipped them, and told you at least one is heads, the probability of them both being heads is 1/3rd.

And yes, the real world data pretty much shows this.

>>17049561
Read >>17049769

retard

>>17049183
The actual question is mr smith with at least one boy born on tuesday asking for the probability of the other child being a boy. There are two issues with the question. First, the wrong answer of 23/27 because Tuesday is irrelevant information. Second, 1/3 and 1/2 are equally valid answers depending on how you approach the problem. 1/3 if you consider the probability of all families with two children and 1/2 if you consider the fact Mr. Smith could be referring to either child A or B when making the "at least" remark.

Another way to think about it:
>1/3:
{BB, BG, GB, GG}
All families of two children are this. If you have a table with every family in the world, remove GG as at least one child is a boy, 1/3rd of the time you get a family with BB.

>1/2:
You have 4 families, one is B1B2, one is B3G1, one is G2B4, one is G3G4. The children mix up at the playground and one boy comes up to you and asks if you think he has a brother or sister. Out of all the boys, half have a brother (B1 and B2 both have brothers while B3 and B4 have sisters).

The least correct answer is 13/27.

>>17049780
P(BB|irrelevant information) must equal P(BB)

Everyone in this thread is retarded.
The probability that both children are boys is zero because all firstborn boys must be sacrificed to Moloch, therefore if Mr. Smith has two children and one of them is a boy, the other must be a girl because if both children were boys then one of them would have been sacrificed and there would only be one child.

What kind of barbarian sacrifices their firstborn son to Moloch? I'm from a much more civilized culture and we used to sacrifice our firstborns to Baal, not Moloch, like some degenerate heathen. But then we developed clone vat technology and determined that children grown in clone vats are not considered to be born, therefore they no longer need to be sacrificed to Baal. Now all children are grown in clone vats.

However, in my civilized culture the probability that Mr. Smith has two male children is still zero because people grown in clone vats are property of the state, therefore this Mr. Smith you speak of must be some kind of pathologically lying thought criminal telling tall tales of "having" children, and he ought to be reeducated with hard labor.

>>17049591
i didn't assume they were causally linked. i'm just counting the number of cases

>>17049783
Why?

>>17048683
The second he changes his phrasing to "One of them is my boy Jim, who was born on Tuesday" the answer becomes 50%

Because people are not interchangable variables

>>17048679
>>17048673
>>17046470
It's roughly 51%
https://ourworldindata.org/grapher/sex-ratio-at-birth
It varies by country but the last name "Smith" implies English ancestry, and Britain has a 51.3% of a baby being a boy

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>>17049763
>The probability of someone having another boy depends on wether or not his other child, who is a boy, was born where time has to be described in minute intervals?
I know this is infinitely confusing for American niggercattle, but probabilities depend on the information in a given context. In this case, you have information that skews second boy/girl cases asymmetrically. It doesn't matter what second variable actually is. It becomes relevant simply by virtue of the condition involving a boy but not a girl.

>>17046455
48% or so.
The more specific the description of the boy, the closer it is to 50%. If you describe the boy perfectly, you're not longer talking about a class, instead it's a specific person. And then you've escaped the conditional probability altogether and it becomes the intuitive 50/50.

>>17049614
>You were not asked whats the chance that a pregnant woman that already had a boy, would have another
Correct. You were asked that if a boy has one sibling, what are the odds that his sibling is also a boy?
50/50.
This is not the Monty Hall problem (which is also mis-stated by brainlets all the time).
ANALOGY WITH CHILDREN BECAUSE THAT'S WHAT THIS IS ABOUT:
Mr. Smith says "I'm picking up my son from soccer practice"
You say "I didn't know you had children"
And he says "Yes, I have 2 kids"

What are the odds that his other child is a boy?
50/50. If that's not accepted a the correct answer then this question was written by the same kind of idiots who keep mis-stating the Monty Hall problem because they don't understand why the original problem has an answer of 1/3

>>17050252
>Correct. You were asked that if a boy has one sibling, what are the odds that his sibling is also a boy?
You're off your meds again and hallucinating a different text than what the OP pic actually says.

>>17050239
can you prove to me why irrelevant information changes a probability? By your logic, the act of flipping a coin when you already have a son changes the probability like stated here: >>17049164

are you autistic?

>>17046455
No. Its unironically /lgbt/.

>>17050292
>can you prove to me why irrelevant information changes a probability?
I know you're a mentally challenged Americoon but didn't I just explain to you what actually makes information relevant in this context?

>>17050292
>By your logic, the act of flipping a coin when you already have a son changes the probability
No, you absolute retard, because then you have additional information tying your FIRST son to that coinflip outcome.

>>17050293
Checked it out, ngl might be smarter on average than /sci based on what I saw

>>17050292
What is your definition of "irrelevant"?

>>17050338
It doesn't matter what his definition of 'irrelevant' is, you braindamaged Mony Hall intellectual. The problem is that he's too inbred to even come up with a valid analogy.

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>>17048741
>It genuinely depends on your sample space.
It genuinely does not.
>In this article >>17046713 ...
[which I literally cited myself to point out that it's a perpetual compost of psychological garbage started by two Israeli psychologists from one of Gardner's several ex post fanbase mishaps]
>... it actually explains it nicely
There is NO interpretation of "Jones family has children, now consider the Jones family's children" that asks you to consider choosing between random families who aren't the Jones family. That is just so incredibly stupid as to merit nothing but scorn, forever.

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>There is NO interpretation of "Jones family has children, now consider the Jones family's children" that asks you to consider choosing between random families who aren't the Jones family.
Imagine being this clinical cretin, writing this completely unironically and STILL being absolutely convinced your IQ is over 80.

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>>17050352
>Indian reply syntax
Imagine still doing this and thinking it doesn't make you look worse lol

>>17050378
>psychotic brown retard mumbles something about its indian brethren after eating breakfast and getting filtered by hypotheticals

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>>17050388
>breakfast delusion
AI or retarded 4chinupper running off AI

>>17050391
>psychotic brown retard literally admits getting filtered by the breakfast question
He probably has some philosophy to explain why that one's invalid, too. Something about israkikes trying to trick him.

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>>17050398
Give me your best synopsis, niglet chink

>>17050400
Of how you'd feel if you hadn't eaten breakfast?

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>>17050401
Sure: how would I feel if I hadn't. Go.

>>17050402
This question is invalid because sub-80 IQs like you are nonsentient therefore 'feel' does not apply in any meaningful sense.

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>>17050404
Sounds like something someone who couldn't other himself into the question would say. Kek

>>17050408
>you couldn't heckin' "other" yourself into being a mindless automaton
So?

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>>17050411
I can; you can't; that's the whole point.

>>17050412
>I can
You've already admitted otherwise by chimping out at the mere mention of a hypothetical.

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>>17050423
You chimped; I asked a question you can't answer because.... you're a C H I ...

>how would you feel if you sampled a different Smith family?
>BUT I DID SAMPLE THE SMITH FAMILY!!!!
Nonwhites can't handle it.

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>>17050430
Nonwhites can't speak English natively. (You)

Whites don't speak English natively. Inbred anglos, Americoon goblins and every other Indian do, though.

>>17050435
>Indian reply syntax

ALL ANSWERS ARE CORRECT 1/3,1/2,13/27 ARE TRUE DEPENDING ON HOW YOU INTERPRET THE SAMPLING PROTOCOL:

> Boolean Interrogation (Autistic mathematician):
\begin{align*}
P(E \mid GG) &= 0 \\
P(E \mid BG) &= \frac{1}{7} \\
P(E \mid GB) &= \frac{1}{7} \\
P(E \mid BB) &= 1 - \left(\frac{6}{7}\right)^2 = \frac{13}{49} \\
P(BB \mid E) &= \frac{P(E \mid BB)P(BB)}{P(E \mid BB)P(BB) + P(E \mid BG)P(BG) + P(E \mid GB)P(GB)} \\
P(BB \mid E) &= \frac{\left(\frac{13}{49}\right)\left(\frac{1}{4}\right)}{\left(\frac{13}{49}\right)\left(\frac{1}{4}\right) + \left(\frac{1}{7}\right)\left(\frac{1}{4}\right) + \left(\frac{1}{7}\right)\left(\frac{1}{4}\right)} = \frac{\frac{13}{196}}{\frac{27}{196}} = \frac{13}{27}
\end{align*}

>Incidental Attribute (Assuming Mr. Smith thought of a specific child when giving you info)
\begin{align*}
P(E \mid GG) &= 0 \\
P(E \mid BG) &= \frac{1}{7} \\
P(E \mid GB) &= \frac{1}{7} \\
P(E \mid BB) &= \frac{1}{7} \\
P(BB \mid E) &= \frac{P(E \mid BB)P(BB)}{P(E \mid BB)P(BB) + P(E \mid BG)P(BG) + P(E \mid GB)P(GB)} \\
P(BB \mid E) &= \frac{\left(\frac{1}{7}\right)\left(\frac{1}{4}\right)}{\left(\frac{1}{7}\right)\left(\frac{1}{4}\right) + \left(\frac{1}{7}\right)\left(\frac{1}{4}\right) + \left(\frac{1}{7}\right)\left(\frac{1}{4}\right)} = \frac{\frac{1}{28}}{\frac{3}{28}} = \frac{1}{3}
\end{align*}

>Random Selection (One time you noticed a boy (who was born on Tuesday) when you went to Mr. Smith's house)
\begin{align*}
P(E \mid GG) &= 0 \\
P(E \mid BG) &= \frac{1}{14} \\
P(E \mid GB) &= \frac{1}{14} \\
P(E \mid BB) &= \frac{2}{14} = \frac{1}{7} \\
P(BB \mid E) &= \frac{P(E \mid BB)P(BB)}{P(E \mid BB)P(BB) + P(E \mid BG)P(BG) + P(E \mid GB)P(GB)} \\
P(BB \mid E) &= \frac{\left(\frac{2}{14}\right)\left(\frac{1}{4}\right)}{\left(\frac{2}{14}\right)\left(\frac{1}{4}\right) + \left(\frac{1}{14}\right)\left(\frac{1}{4}\right) + \left(\frac{1}{14}\right)\left(\frac{1}{4}\right)} = \frac{\frac{2}{56}}{\frac{4}{56}} = \frac{1}{2}
\end{align*}

>>17050495
oops:

> Boolean Interrogation (Autistic mathematician):
[eqn]
\begin{align*}
P(E \mid GG) &= 0 \\
P(E \mid BG) &= \frac{1}{7} \\
P(E \mid GB) &= \frac{1}{7} \\
P(E \mid BB) &= 1 - \left(\frac{6}{7}\right)^2 = \frac{13}{49} \\
P(BB \mid E) &= \frac{P(E \mid BB)P(BB)}{P(E \mid BB)P(BB) + P(E \mid BG)P(BG) + P(E \mid GB)P(GB)} \\
P(BB \mid E) &= \frac{\left(\frac{13}{49}\right)\left(\frac{1}{4}\right)}{\left(\frac{13}{49}\right)\left(\frac{1}{4}\right) + \left(\frac{1}{7}\right)\left(\frac{1}{4}\right) + \left(\frac{1}{7}\right)\left(\frac{1}{4}\right)} = \frac{\frac{13}{196}}{\frac{27}{196}} = \frac{13}{27}
\end{align*}
[/eqn]

> Incidental Attribute (Assuming Mr. Smith thought of a specific child when giving you info)
[eqn]
\begin{align*}
P(E \mid GG) &= 0 \\
P(E \mid BG) &= \frac{1}{7} \\
P(E \mid GB) &= \frac{1}{7} \\
P(E \mid BB) &= \frac{1}{7} \\
P(BB \mid E) &= \frac{P(E \mid BB)P(BB)}{P(E \mid BB)P(BB) + P(E \mid BG)P(BG) + P(E \mid GB)P(GB)} \\
P(BB \mid E) &= \frac{\left(\frac{1}{7}\right)\left(\frac{1}{4}\right)}{\left(\frac{1}{7}\right)\left(\frac{1}{4}\right) + \left(\frac{1}{7}\right)\left(\frac{1}{4}\right) + \left(\frac{1}{7}\right)\left(\frac{1}{4}\right)} = \frac{\frac{1}{28}}{\frac{3}{28}} = \frac{1}{3}
\end{align*}
[/eqn]

> Random Selection (One time you noticed a boy (who was born on Tuesday) when you went to Mr. Smith's house)
[eqn]
\begin{align*}
P(E \mid GG) &= 0 \\
P(E \mid BG) &= \frac{1}{14} \\
P(E \mid GB) &= \frac{1}{14} \\
P(E \mid BB) &= \frac{2}{14} = \frac{1}{7} \\
P(BB \mid E) &= \frac{P(E \mid BB)P(BB)}{P(E \mid BB)P(BB) + P(E \mid BG)P(BG) + P(E \mid GB)P(GB)} \\
P(BB \mid E) &= \frac{\left(\frac{2}{14}\right)\left(\frac{1}{4}\right)}{\left(\frac{2}{14}\right)\left(\frac{1}{4}\right) + \left(\frac{1}{14}\right)\left(\frac{1}{4}\right) + \left(\frac{1}{14}\right)\left(\frac{1}{4}\right)} = \frac{\frac{2}{56}}{\frac{4}{56}} = \frac{1}{2}
\end{align*}
[/eqn]

>retarded token-"thinking" mathlets philosophizing about "interpretations" of a straightforward conditional probability problem
New voting test dropped:

You are given a list of all the Smith families in [insert your braindamaged country's name]. Each item lists the family's children and the weekyday of each child's birth. Circle all the Smith families with two children, at least one of whom is a boy born on Tuesday.

>>17050347
>that asks you to consider choosing between random families who aren't the Jones family
in both instances ie the one that gives 1/2 and the one that give 13/27 (or 1/3 if no tuesday information) you are sampling families; what else would you sample?
In any case it's literally written in the article you claim to have posted:
https://en.wikipedia.org/wiki/Boy_or_girl_paradox#Second_question
>But they lead to different correct answers:
>*From all families with two children*, at least one of whom is a boy, a family is chosen at random. This would yield the answer of 1/3.
>*From all families with two children*, one child is selected at random, and the sex of that child is specified to be a boy. This would yield an answer of 1/2.
it's the same for the one with the tuesday information
>Suppose we were told not only that Mr. Smith has two children, and one of them is a boy, but also that the boy was born on a Tuesday: does this change the previous analyses?
>Again, the answer depends on how this information was presented – what kind of selection process produced this knowledge.
that's what sampling means...

>>17050657
Brainlet cope. The problem is completely unambiguous about what the subset of families can be sampled from: those with two children, at least one of whom is a boy born on Tuesday. Those are the conditions that specify the Smith family. There is nothing to discuss. There is one answer and everything else is failed wordcel cope.

>>17049572
>only 6 ways this can happen because the boy cannot also be born on tuesday
Yeah he can, the problem posits "at least one is a boy born on a tuesday", not "at least one is a boy, born on a tuesday". The punctuation matters here.
The other can also be a boy born on a tuesday.
Which means there are 7 different ways for 2 boys to be born.

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>the problem posits "at least one is a boy born on a tuesday", not "at least one is a boy, born on a tuesday".

>>17046455
Zero percent, because they will troon out anyway

If your answer isn't 51% and some change, you are not getting the job, becausd this isn't a math exercise and you're expected to recognize that.

>>17048741
>if the question is interpreted as "From all families with two children, at least one of whom is a boy, a family is chosen at random"
*born on tuesday I meant ofc; otherwise its 1/3

>>17050942
>I'll simply note that any deviation from 1/2 is an ESL fantasy
>The problem is completely unambiguous about what the subset of families can be sampled from: those with two children, at least one of whom is a boy born on Tuesday.
With the sample space you mention, namely \( (\{boy,girl\}\times\{1,2,3,4,5,6,7\})^2\), you get 13/27. It is with \( (\{boy,girl\}\times\{1,2,3,4,5,6,7\})^2\times\{1,2\}\) that you get 1/2 (as I wrote here >>17048741).
--
Here is the calculation: set \( P=\frac{|A|}{196}\) for all subsets \( A\) of \( \Omega=(\{boy,girl\}\times\{1,2,3,4,5,6,7\})^2\); then
\( P(\textrm{both boys}|\textrm{at least one kid is a boy born on T})=P(\textrm{both boys}\cap\textrm{at least one kid is a boy born on T})/P(\textrm{at least one kid is a boy born on T})=\frac{49-6^2}{196-169}=\frac{13}{27\)
Feel free to show how you get 1/2 with the sample of families "with two children, at least one of whom is a boy born on Tuesday". And make sure to write down precisely what your \( \Omega\) is (and maybe next time think and learn to read before calling others name).

>>17051181
>With the sample space you mention
That's the only sample space the problem mentions. Ifi n doubt, please do the retard screening test here: >>17050508

Also why are you attributing that angloon golem mental retardation quote to me? That's nowhere in my post.

The question is asking the probability that the sex of one child is a male. It's a given that the other child is male, and the order does not matter. I see anons listing out BB, BG, GB etc but in this case BG and GB are not two separate events. Regardless of what outcomes you want to list, you end up with the probability that a child is a boy or a girl, which is 1/2, or 51% if you want to use a real world statistic. The order only matters if you assume that the sex of each child are not I.I.D. events. The Tuesday thing is completely irrelevant. This isn't a math problem, this is a problem to test how well you can read and comprehend.

>>17051434
>The question is asking the probability that the sex of one child is a male
Whose child?

>>17051443
Your wife's boyfriend's.

>>17051454
The sex of the child would then depend on whether the cuck was gifted a nintendo switch by the bull

>>17046455
Yeah

>>17049564
It should be easy to figure out at least intuitively why it matters if you consider the opposite case.
What if you got this instead
Mr. Smith has two children. What is the probability that both children are boys.
Now that we have even less information the chance of both of them being boys is 1/4th because both children are random.
If we get additional information that one of them is a boy it increases to 1/3rd because you have some information about one of the children but don't know which one
If we get more specific information like the Tuesday birthday it raises up to 13/27 because the chances of two Tuesday births is very rare but not impossible.
If we got even more information like one is a boy born on Tuesday that has won the Olympic bronze in 100m swimming and is left handed the chances would be pretty much 50/50 because there's pretty much 100% chance that there's just one of those around.

Information that applies to potentially both children is less valuable than something that applies to only one. Tuesday birthday is rarer than being a boy so it's more likely that it applies to a specific child and as soon as you have a specific child the other child is just 50/50 because the events are independent.

>>17046482
kek
pythonbros lose yet again

>>17048725
it's awesome because you could gather a million familes with 2 children and at least 1 boy, and arbitralily claim the odds of a second boy are lower, and just be wrong

>>17046455
Is my job to analyse Mr. Smiths and determine the probability of the gender of his children? If not then who gives a shit?

>>17049164
>"Assuming both genders are equally likely, 1/3. (BB, BG, GB)"
we dont know if the boy we know about is older or younger, so you must double the BB
(capital is the boy we know about) here are the possibilities:
Bb, Bg, gB, bB

>>17046713
Actual "Train A is traveling X mph, Train B is traveling Y mph, what color is Train A" bullshit mathematics.

Let [math]X[/math] be the number of boys, and [math]Y[/math] be the number of boys born on Tuesday. We can treat each of these as binomial random variables with [math]n=2[/math] and probabilities [math}p_1[/math] and [math]p_2[/math], respectively. It is clear that "boy born on tuesday" is a proper subset of "boy". Thus:

[eqn]\mathbb{P}(X=2|Y\geq1) = \frac{\mathbb{P}(X=2 \ \cap \ Y\geq 1)}{\mathbb{P}(Y\geq 1)}[/eqn]

[eqn]\mathbb{P}(X=2|Y\geq1) = \frac{2p_2(p_1-p_2)+p_2^2}{2p_2(1-p_2)+p_2^2}[/eqn]

[eqn]\mathbb{P}(X=2|Y\geq1) = \frac{2(p_1-p_2)+p_2}{2(1-p_2)+p_2}[/eqn]

[eqn]\mathbb{P}(X=2|Y\geq1) = \frac{2p_1-p_2}{2-p_2}[/eqn]

Given that there are roughly 105 men for every 100 women (https://ourworldindata.org/gender-ratio), we can let [math]p_1=\frac{105}{205}=\frac{21}{41}[/math]. We may assume that there's a [math]\frac{1}{7}[/math] chance for a baby to be born on a Tuesday (I suspect it may be slightly higher than this, since some pregnancies have an induced labour, and this is more likely to be done on a weekday than on a Saturday or Sunday). Thus [math]p_2=\frac{1}{7}p_1=\frac{21}{287}[/math].

Substituting these values in yields

[eqn]\mathbb{P}(X=2|Y\geq1) = \frac{39}{79}[/eqn]

>>17046455
in the math world:
7 days of week, 2 genders, 2 children = (7 * 2)^2 possible states; ((boy, tuesday), (girl, wednesday)), ...
at least one must be (boy, tuesday) to satisfy the prior. This gives 14 + 14 = 27 possible states; other girl: 7 * 2 + other boy: 7 * 2 - 1 state to account for ((boy, tuesday), (boy, tuesday)) symmetry- otherwise we count (boy, tuesday) twice. Counting these states, 13 satisfy the condition given in the question.

This gives our answer as 13/27.

in the real world:
probability of twins is 1.2%
probability of being same gender when twins is 66%
probability of gender doesn't change across days of the week
probability of being born male is 53%
0.53 * 0.988 + 0.66 * 0.012 = 53.2%

[eqn]
\texttt{from random import choice}\\
\texttt{runs = 0}\\
\texttt{both_boys = 0}\\
\texttt{while True:}\\
\;\;\;\;\texttt{# Mr Smith has two children}\\
\;\;\;\;\texttt{# generate children}\\
\;\;\;\;\texttt{children = [choice(["boy", "girl"]) for _ in range(2)]}\\
\;\;\;\;\texttt{# At least one is a boy born on Tuesday}\\
\;\;\;\;\texttt{# generate birthdays}\\
\;\;\;\;\texttt{birthday = [choice(["sun", "mon", "tues", "wednes", "thurs", "fri", "satur"]) + "day" for _ in range(2)]}\\
\;\;\;\;\texttt{if not any(children[i] == "boy" and birthday[i] == "tuesday" for i in range(2)):}\\
\;\;\;\;\;\;\;\;\texttt{# if problem statement is not satisfied, don't count this run}\\
\;\;\;\;\;\;\;\;\texttt{continue}\\
\;\;\;\;\texttt{runs += 1}\\
\;\;\;\;\texttt{if all(children[i] == "boy" for i in range(2)):}\\
\;\;\;\;\;\;\;\;\texttt{both_boys += 1}\\
\;\;\;\;\texttt{if runs % 100000 == 0:}\\
\;\;\;\;\;\;\;\;\texttt{print(f"{runs}: {both_boys / runs}")}\\
[/eqn]
I get 0.481533 after 5 million runs... wtf? Can someone explain where is the mistake in my code?

>>17050240
>instead it's a specific person
Of course it's a specific person, retard. It's one of Mr. Smith's kids.

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>>17053558
WTF are you throwing the dice instead counting all possibilities, do you understand the meaning of uniform distribution?

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>>17050984

"well actually the odds of being a male are 51%" poster are the actual worst posters itt

Two children, at least one is boy, P both boys = 1/3

Two children, at least one is boy whose favorite number between 1 and positive inf is 1, P both boys = 1/2

Make it make sense

It's 50/50, all the probability space bullshit is a red herring. The 1/3 coin flip HH TH HT TT example is one of the most retarded things I have ever read

>>17054344
is the coin flip version also 50/50?

>>17054344
it's not, it's closer to something like 51.5%

>>17049564
>Can someone explain succinctly and without using ad hominem why the "Tuesday" part is at all relevant to the sex of the other child?
Tuesday isn't relevant in and of itself. The fact that you're filtering the relevant cases based on a condition that involves one sex but not the other is relevant because it introduces an asymmetry.

You'd think at some point the geniuses at these companies would realise that using famous probability questions with a time limit to filter your candidates will just give you people who know the answer because they've encountered the question before.

>>17054783
they don't care

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>>17056459
Maybe they would beat the market better if the interview question were something like "explain the limits of cash flow analysis" and they didn't just hire quants.

>>17046671
The bigger real-world error is that boy girl probabilities are not 50/50. Girls have a probability of .485 or nearabouts but it is strictly not .5, this is because of how genes work. it also assumes both child sexes are independent/exchangeable events (they are not).

>>17050338
Irrelevant means it is outside the pertinent lightcone, or otherwise has no discernible causual relationship

>>17054344
It's a trick.

If you flip two coins and look only at one and that one is heads that doesn't make it more likely that you flipped two heads since the coin flips were independent.

It also doesn't make it more likely that when you look at the other coin it too will also be heads, for the exact same reason, so long as you are fair / equally likely to look at either coin and have no magical ability to pick out heads more than tails.

However the Bayesian will say that the assigning of which coin to be the first is not a foregone conclusion even though you have picked a coin first and looked at it first. Therefore they will consider that there are three situations where you look at heads first: HT, TH, HH, where HT is heads first and TH is tails first. So to them, not only are you equally likely to pick the first coin first as the second coin first (utter nonsense devoid of semantic meaning) but you don't actually know which of the first and second coin you picked first (yet another semantically illogical claim, although it matters little when both are heads). So to them you are in one of three equally likely situations, and thus they say 1/3. It is indeed a wittgenstein word game.

>>17056866
Do the test, brainlet: >>17050508

>>17056866
To add to this, a more sane person would object and say, there is no way of picking the second coin first, and so the only situations left are HT and HH, which corresponds to 1/2, which is precisely the chance that the second coin lands heads up.

>>17056867
The point is that Bayesian probability is not commensurate with the probability of reality since it must allow free reordering of the past and future to compute its probabilities, while reality does not allow this since entropy exists.

>>17056872
Do the test, brainlet. There's nothing "Bayesian" about it. Can you circle the correct items and then answer a frequentist question about them?

>>17056877
It is Bayesian because it gives a conditional probability, which was invented by Thomas Bayes.

>>17056880
>circling the correct Smiths is Bayesian
You're literally mentally ill, not just profoundly retarded.

>>17056883
I'm not falling for your Wittgensteinian word game. It makes unrealistic Bayesian assumption that my inability to follow instructions is not a foregone conclusion, even though you have necessarily picked the dumbest moron in the thread.

>>17056883
Bayesian truly are incommensurate though. They don't even have the same units. It's like comparing Kilonewtons to the number 2.

>>17056891
>i can't decide if an item on the list fits the criteria or not because it's too Bayesian and incommensurate with my intellectual abilities

That'd be >>>/diy/
/sci/ would have a claim if a majority of people knew the basics of the things they flame about, but they don't so it's disqualified.

>>17057582
yeah, one half of sci is trolling and the other is genuinely retarded, and neither of them is aware of which half they are

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Holy shit I get it bros. It's all about the selection. I take all the families in my city, and I want to find the families with two children, at least one of whom is a boy born on a Tuesday. As I filter by these three criteria, the proportion of families with two boys will change.

I start by dropping all families which do not have two children. I am left with 1/4 BB, 1/4 GG, and 1/2 mixed families. I then drop all families which do not have at least one boy, and the proportion of families remaining which have two boys now raises to 1/3. If I then filter by the final criteria, dropping every family who do not have at least one of those boys born on a Tuesday, it is *more likely* for the families with two boys to meet that criteria than the families with only one boy (simply because they have two chances), so proportionally more of the one-boy families will be dropped. And as it happens the proportion of two-boy families, just as it raised from 1/4 to 1/3 when selecting for families with at least one boy, will raise from 1/3 to 13/27.

Literally all it comes down to is that two-boy families are overrepresented in this selection, i.e. it's more likely for a randomly chosen family in this selection to have two boys than in the selection which did not include a specific day of the week (or any other arbitrary criteria), because it was more likely for a two-boy family to meet the arbitrary criteria than for a one-boy family to meet it. It actually makes sense.

>>17059547
Suppose you had the set of all tuples where one boy is born on x day of the week. By symmetry each would have the odds you listed. What is the math to recover 100% of the babies based on your odds? If there is a million samples and for any given day 13/27 has 2 boys. And 14/27 has a boy and a girl. But it has already selected out 25% of the population, and they were all girls. So the remaining population is 2/3 boys. Given the above, the math seems to indicate your population is sampling boys very high.

>>17046455
We use the condition of one boy being born on a Tuesday to exclude some scenarios, which increases the probability of the other child being a girl.
Without that condition the chance is 1/2.
I don't like this intentionally confusing example.
It assumes a simplification of sex-determination, doesn't tell the reader about it and expects them to also assume that simplification.
What happens when the interviewee knows that more boys than girls are born?
Taking complex real processes, deriving from them simplified statistical models, then assuming them to be true, rather than approximations, is one of the major reasons for the reproducibility crisis.
This is mathematically correct, but cognitively harmful if framed carelessly.

>>17059547 passes the brown filter here: >>17050508
>>17059569 still can't follow basic instructions.

>>17049572
You're miscounting, it's 7 for each case and the day doesn't matter
>A boy on tuesday and a boy on tuesday
The one we know about could be either first or second, you're making a mistake by treating this as one case.
Therefore, the possibilities are
>The boy we know to have been born on Tuesday, and another one born on any day of the week
7 cases
>One boy born on any day of the week, and the one we know to have been born on Tuesday
7 cases

Because all cases are equally likely, you can ignore the stipulation that the boy we know about was born on a Tuesday. The answer is 1/3.

>>17051540
>If we get more specific information like the Tuesday birthday it raises up to 13/27 because the chances of two Tuesday births is very rare but not impossible.
Two Tuesday births are exactly as likely as any other combination of weekdays involving at least one Tuesday. It's basically the same question again.

>>17056866
You're the only one playing stupid word games here, by making one coin "first" simply because it's the one you have information about. A semantic trick.

>>17059604
>a semantic trick
There's no semantic trick in this post. He's quite simply retarded and can't tell the difference between "one of two coins came up heads" and "the first of two coins came up heads". The semantics for both of these statements are very clear, he's just getting filtered by 3rd-grade-level reading comprehension.

>>17059547
Dang, I do believe you're right. I set out to disprove you by making a spreadsheet with all possible cases, but then I arrived at 13/27.

Ignore >>17059591 and >>17059601, I was wrong.

Why inform us it was on a Tuesday lmfao

American math problems aren’t even difficult in essence they’re only made difficult due to retarded communication when setting the problem up with lots of ambiguity

>>17054783
Lmao

>>17059655
>Why inform us it was on a Tuesday lmfao
Which day would you rather it be, retard? It needs to be some constant, but if the problem said "day X" someone like you would probably try to solve for it.

>>17047356
Then why you tell me bitch? Why you waste my time?

>>17059667
This is exactly my point

Mathematics in America isn’t about using methods to solve problems it’s about “tricking” with oddly phrased text and ambiguous wording to intentionally make people get it wrong

It is very strange

>>17059715
>This is exactly my point
Your point is that you have profound mental retardation and can't into high school math no matter how the question is phrased?

>>17059747
No, the point is the questions should be phrased correctly, but they rarely are in America.

>>17046455
100 niggers in your ass

>>17046455
>>17060383
Fuck meant 50

>>17059823
The question is phrased correctly if you speak English.

>>17059823
>the questions should be phrased correctly
How do you want it to be phrased, retard? Protip: you won't give a straight answer.

>>17046455
650000 a year is 0.0868 dollars per second
thats 7.812 dollars for this problem.
If that's the cost of solving this problem, the upside must be shit.
i delegate to a junior.


repeat for every problem

>>17050234
England is full of pakis who abort daughters

>>17046455
It's not the dumbest board but the undergads and schizos drag it down the smartest board is still probably some hobby board like /po/

>>17047306
if it didn't the information wouldn't be part of the problem statement

>>17046455
It basically depends on whether or not you were going to be given the information regarding whether or not one of them is a boy born on a Tuesday in either case. If you were, then the information you're receiving is meaningful to your perception of the events having occurred and the answer is 13/27. But if you've simply received information regarding one of the two children, then clearly it's still a 50% chance.

>>17046455
Why is the day of the week relevant to anything?
population birth sex ratios are about the only thing relevant here and the low risk of identical twin boys either way it's near 50% but not exactly depending on the birth ratio data.

>>17046455
>Is /sci/ the smartest board on 4chan?
absolutely not
even the gay retard boards are probably smarter

If you only have 90 seconds, you need to already know the answer, which is not unreasonable, because everyone has already heard of it, and anyone with an interest in probability will have actually worked it out

But that does mean it's not a question that you're actually supposed to solve in 90 seconds

>>17053273
u forgot the probability of triplets and quadruplets, fagit