[stupac2]

I used R's binomial distribution:

Code:

> pbinom(3, 50, 1/350, F)



[1] 1.381674e-05

BC

That's bizarre, I'm doing the same thing but in excel and getting a much different result. Although I think it's a difference in the cumulative/individual behavior, I can get that value if I switch to "=1-BINOM.DIST(3,50,1/350,TRUE)", which is "the odds that there are greater than 3 successes in 50 tries", clearly not what we actually want here, which is more like "the odds that there are at least 3 successes in 50 tries".



Incidentally, one of the reasons that I thought this couldn't be all that unlikely is the birthday problem, which has pretty similar numbers (in case you're unaware, that's the result that the number of people needed before there's a 50% chance of a duplicate birthday is a lot lower than you'd guess, like 35). 1/350 is about 1/365, 50 is bigger than 35, and you're switching the 2 to a 3. Now obviously it's a bit less likely because not everyone has a 1/350 disease and you're not looking for any match, but I wouldn't expect that to be a 4 orders of magnitude reduction in odds.

[stupac2]

I used R's binomial distribution:

Code:

> pbinom(3, 50, 1/350, F)



[1] 1.381674e-05

BC

That's bizarre, I'm doing the same thing but in excel and getting a much different result. Although I think it's a difference in the cumulative/individual behavior, I can get that value if I switch to "=1-BINOM.DIST(3,50,1/350,TRUE)", which is "the odds that there are greater than 3 successes in 50 tries", clearly not what we actually want here, which is more like "the odds that there are at least 3 successes in 50 tries".



Incidentally, one of the reasons that I thought this couldn't be all that unlikely is the birthday problem, which has pretty similar numbers (in case you're unaware, that's the result that the number of people needed before there's a 50% chance of a duplicate birthday is a lot lower than you'd guess, like 35). 1/350 is about 1/365, 50 is bigger than 35, and you're switching the 2 to a 3. Now obviously it's a bit less likely because not everyone has a 1/350 disease and you're not looking for any match, but I wouldn't expect that to be a 4 orders of magnitude reduction in odds.