In humans, hemophilia is caused by a recessive allele on the X chromosome. Suppose a man with hemophilia has children with a healthy woman whose mother had hemophilia. What is the probability that their second child will have hemophilia? (Enter the probability as a percent. Enter the number only without the percent sign. For example, enter 100% as 100 and enter 12.5% as 12.5)

The answer is 50

Explanation:

Hemophilia is a X-linked disease. That means the recesive allele which causes the disease is not in Y chromosome, but only in X chromosome. If we denote:

X⁺ : dominant allele

X⁻: recesive allele

Then, in a woman there are three posibilities:

X⁺X⁻: is a carrier woman (without hemophilia)

X⁺X⁺: healthy woman

X⁻X⁻: woman with hemophilia

But in a man there are two posibilities:

X⁺Y: healthy man

X⁻Y: man with hemophilia

A man with hemophilia is X⁻Y, and a healthy woman whose mother had hemophilia is a carrier woman (X⁺X⁻). If they have a child, there are 4 posibilities, and each one has 1/4 of occurrence probability:

X⁻Y x X⁺X⁻ = X⁻X⁺, X⁻X⁻, X⁺Y, YX⁻

Posibilities with hemophilia are X⁻X⁻ and YX⁻ (1/4 + 1/4 = 1/2 = 0.5 = 50%)

In each filial, there is a 50 percent of probability of having a child (man or woman) with hemophilia.