Your math is wrong. The probabilities you listed for the 2 events is correct, but you multiplied 0.72 by 0.03,but probabilities aren't stated that way. 0.72% is

Your math is wrong. The probabilities you listed for the 2 events is correct, but you multiplied 0.72 by 0.03,but probabilities aren't stated that way. 0.72% is a probability of 0.0072 and 0.03% is 0.0003. So the correct probability of coincidence is much lower than 0.02% it's 0.0002% or a probability of 0.000002. So that rate wouldn't be 2 in 10,000 it should be 2 in 1,000,000. This pravelance rate is therefore 25 times lower than that of childhood onset schizophrenia (1 in 40,000). You did however get the number of people who should have it in the US correct at roughly 620 cases if the two conditions are independent. Although that only includes the reported population numbers, as a better population estimate to account for people who won't answer the census is more like 340 million. This portion of the population that doesn't answer the census could easily be hiding all 670 potential cases because they also don't tend to trust doctors and would never be diagnosed. I'm not saying that this is a guaranteed scenario, but schizophrenia does have a genetic component, so it is possible that we simply haven't seen the cases in the general population because their families have hidden the affected family members. The "closet" syndrome when it comes to mentally ill family members is well documented, and some groups have even been known to hide family members with physical disabilities such as blindness or deafness. We believe this is happening less today, but that's difficult to prove and may simply be our way of coping with the fact that we will never be able to help people trapped in that situation.