Question

A man with hemophilia (a recessive, sex-linked condition) has a daughter without the condition. She marries a man who does not have hemophilia. What is the probability that their daughter will have hemophilia? Their son? If they have four sons, what is the probability that all will be affected?

Short answer

The probability that the daughter will be hemophilic is zero because neither of her parents is affected.

The son's probability of hemophilic is half (1/2) as they might receive a defective allele from their carrier mother.

The probability that all four will be hemophilic is 1/16 because each son has ½ probability of being hemophilic.

Step-by-step solution

Explanation for the probability that the daughter will be hemophilic

Hemophilia is an X-linked recessive disease. This meansa male with a hemophilic X chromosome will acquire the disease because males have one X and one Y chromosome.

Females with two hemophilic X chromosomes will acquire the disease as they have two X chromosomes. However, with one hemophilic X chromosome, they will be a carrier for the disease.

Here, the man is hemophilic, so he would transmit his hemophilic X chromosome to his daughter. Thus, her daughter must be the carrier for the disease as she is not hemophilic.

When the carrier woman marries a normal male, their daughter's chance to be hemophilic is zero.This is because the daughter must receive a hemophilic X chromosome from both the parent to be hemophilic.

However, this is not possible because his father does not have the defective allele for the trait.

Explanation for the probability that the son will be hemophilic

The males receive their X chromosome from their mother.Here, the mother being a carrier, can transmit either the normal X chromosome or hemophilic X chromosome to the son.

This means there is a 50 percent chance that the son might inherit the hemophilic X chromosome. Thus, the probability that the son is hemophilic is ½ because he has half chance of inheriting the hemophilic X chromosome from the mother.

Probability that all four sons will be hemophilic

The probability that the son would be is ½. There are four sons, so the likelihood that all four sons will be hemophilic can be calculated as $\frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}=\frac{1}{16}$.

Therefore, the probability that all the sons will be hemophilic is 1/16.