Just to be clear, this is not homework. Suppose a biological family has five children, two of whom have a certain recessive genetic disorder that is not sex-linked. The parents themselves do not have this disorder. I want to estimate the probability that the parents are carriers. How can I do that, short of getting this probability directly from a lab study?
This problem appears to be where Bayesian statistics can help. All I need to know is: 1) the probability of the parents being carriers, given they don't have the disorder, but 2/5 of the children do. 2) The probability of the parents being carriers and 3) The probability of the children having the disorder.
3 I can probably find without too much effort. #2, I'm guessing, is a Hardy-Weinberg problem - I just need to find the relevant statistics for people of the parents' backgrounds. But I have no clue how to start with #1.