Since you put in all the work! It's the binomial distribution [1]. What you've done is to simulate the distribution of a sum of binomial distributions. Your po

Since you put in all the work! It's the binomial distribution [1]. What you've done is to simulate the distribution of a sum of binomial distributions. Your point of there being more than two types of rare cancer and that any selection of outliers over all the types would give rise to the same sentiment is totally correct. I did the quick mental calculation with one in a million. As you see in your simulation the difference between 1e-5 and 1e-6 makes all the difference here. [1] https://en.m.wikipedia.org/wiki/Binomial_distribution https://en.m.wikipedia.org/wiki/Binomial_distribution