If a number lottery has a winning chance of 1:1000000, does buying 100 tickets make the chance 1:10000 or 1:999900?Please be patient, I'm dumb and don't get probability and statistics. (as should be evident by the fact I'm willing to throw money at a lottery)
>>17066561the second one, then the first.
Chance of winning 1 lottery is p = 1/1000000 (so chance of losing 1 lottery is q = 1 - p).So, there are two possibilities.A: win at least 1 out of 100 ticketsB: win 0 out of 100 ticketsThe probabilities of all possible events sum to 1. As A and B cover all possible events and don't overlap, it must mean that P(A) + P(B) = 1. P(B) = q^100 (because we must lose all 100 lotteries and we assume each ticket is independent).Thus, P(A) = 1-q^100 = 1 - (1 - p)^100 = 0.0000999505... which translates to roughly a 1:10000 chance of winning at least 1 ticket.Though note that when we assume that each ticket is independent in B, this is not actually true because if you buy 1 ticket, that means there is one less losing ticket available so the next ticket has a slightly higher chance of winning but it is neglibile for the odds you gave.
>>17066564Thanks!
>>17066561The important take here is that even though 1/10000 just visually looks much better than 1/1000000, it's still very shit odds.
>>17066564This is for the “British Lottery”.The “American Lottery” uses a different calculation.
