Question

Albinism in humans is autosomal and fully recessive to normal color. A couple, who are both normal have a daughter who is albino; they want to have 3 more children. What is the probability that they will have 3 normal girls?

Answer 1

Because the parents, both non-albino, had an albino child, you know that they are both heterozygotes for the albino trait. The probability that any given child is albino will then be \(25\%\), and \(75\%\) for a "normal" child.

The child's sex is independent, so\[\mathbb P(\text{normal}\land\text{girl})=\mathbb P(\text{normal})\mathbb P(\text{girl})=75\%\times50\%=37.5\%\]The chance of having three such girls is then\[\left(\mathbb P(\text{normal}\land\text{girl})\right)^3\approx5.3\%\]