In essense, for the gene in question, each horse is either AA, CA or CC. (As usual, the foal gets one gene from each parent) Several houndred horses have been tested so there are a lot of observations. 30 foals (children) of one stallion (male horse) has been tested, and 10 are CA while 20 are CC. Since that stallion has CC foals I know he must be CA or CC. Since there are so many CC foals, that seems most likely. Unfortunately we don't know the genes of the mothers, but the population is 11 % AA, 20 % CC and 69 % CA so I guess we can just assume the 30 mothers are distributed according to this.

So how do I calculate the posterior probability that this stallion is CC? I suspect I have to use Bayes' Theorem in one form or another but I will reluctantly admit that I am not sure how to apply it and how to define the terms correctly. The strange part is that at some point I was actually relatively comfortable with this, but I have forgotten quite a bit as I never use this part. So any and all input is greatly appreciated!