Question

In humans the sex of an individual is determined by the sex chromosomes that they inherit. All individuals carry two sex chromosomes, but males carry a so-called X and a Y chromosome (and are thus called XY) whereas females carry two X chromosomes (and are thus called XX). When a male and female produce an offspring, each gives the offspring one of its sex chromosomes, chosen with equal probability. Thus, a child always inherits an X chromosome from its mother since, regardless of which of her sex chromosomes is chosen, it will always be an X. But the child inherits the X chromosome from its father with probability 1/2 (in which case it will be female) and the Y chromosome from its father with probability 1/2 (in which case it will be male).

Muscular dystrophy is a genetic disease caused by a mutation on the X chromosome. During reproduction this mutation arises spontaneously on each of the X chromosomes of the parents independently, and with probability μ. We can therefore view the production of a child as consisting of two probabilistic experiments. First, one of the two sex chromosomes is chosen with equal probability from each parent. Second, for each X chromosome that is chosen, the muscular dystrophy mutation arises with probability μ. All male children carrying the mutation will have muscular dystrophy whereas only females whose X chromosomes both carry the mutation will have the disease.

What is the probability that the child will have the disease, given that it is a male?

Answer 1