The color of a persons eyes is determined by a single pair of genes. If they are both blue-eyed genes, then the person will have blue eyes. If they are both brown-eyed genes, then the person will have brown eyes. Also, if one of them is a blue-eyed gene and the other a brown-eyed gene, then the person will have brown eyes.
A newborn child independently receives one gene from each of his parents and the gene it receives from a parent is equally likely to be either of the two eye genes of that parent.
Suppose that Joe and both his parents have brown eyes, but Joe's sister and Joe's wife Claudia have blue eyes.
(a) What is the probability that Joe possesses a blue-eyed gene?
(b) What is the probability that Joe and Claudia’s first child will have blue eyes?
(c) If Joe and Claudia’s first child has brown eyes, what is the probability that their next child will also have brown eyes? (Hint: This is not the same as one minus the answer to part (b)).
How to solve part(c)? Suppose we let E1=(the first child has brown eyes),E2=(the next child has brown eyes) How to calculate Pr(E2|E1)?