>>12311350Your way might work, using the total vote count for the state as your N, the votes for biden in the state as K, and the 100k as your sampling size with k number of successes. The geometric distribution would be fair there.
However, I don't think you'd really prove much with that. There may be other reasons why a batch of mail in ballots would be biden favored rather than fraud. Because of the politics around mail in voting, you shouldn't assume that a sample of mail in ballots is truly a random sample from the state voting distribution.
You may have better luck using a binomial distribution with a p determined by mail-in ballot biden/trump ratio from other other states.
Or you could try using the hypergeometric but with the states mail in ballot total for N and state mail in for biden as K. Then, the sample would be chosen from that pool.
At the end of the day, you need a good comparison to make a compelling argument. Im struggling to think what that would be. Mail-in ballots from other states would be good, but the p is definitely going to change by region. It's not enough to say that the event is super improbable. You have to say the event is super improbable compared to real data collected in a similar manner.
