I didn't open my stats book to confirm this, but my hunch is that you can estimate the likelihood of what we observe (0/300M) with what we expect (600/300M) in

I didn't open my stats book to confirm this, but my hunch is that you can estimate the likelihood of what we observe (0/300M) with what we expect (600/300M) in the following way. Think of 1 six sided die. The odds of not rolling a six is 5/6. In two rolls, the chance of not seeing a six is 25/36, in 3 rolls (5/6)^3. At 4 rolls, the odds of not ever rolling a 6 are 0.47, at 20 rolls 0.02 and at 30 rolls 0.004. So in this case, the category is being both born blind and developing schizophrenia. The odds of a single person being in this category are 2/1M, and the odds of a person not being in the category are 999998/1M. The expression for never observing a person in the category for a population of 300M is ((10^6-2)/(10^6))^(300x10^6). Wolfram Alpha says this is equal to 2.6x10^-261. It is very unlikely that the two distributions for blindness and schizophrenia are independent!