Question

Imagine that you are a genetic counselor, and a couple planning to start a family comes to you for information. Charles was married once before, and he and his first wife had a child with cystic fibrosis. The brother of his current wife, Elaine, died of cystic fibrosis. What is the probability that Charles and Elaine will have a baby with cystic fibrosis? (Neither Charles, Elaine, nor their parents have cystic fibrosis.)

Short answer

The probability that Charles and Elaine's child will have cystic fibrosis is 1/6.

Step-by-step solution

Cystic Fibrosis

Cystic Fibrosis (CF) is a genetic disorder that is caused due to a defect in the CFTR gene. It affects the lungs, and individuals have breathing difficulties due to the build-up of mucus. It is an autosomal recessive disease.

An individual must inherit two copies of the defective gene to be diseased with CF. However, individuals with one copy are the carriers of the disease.

The genotypes of Charles (father) and Elaine (mother)

Let C be the normal allele and c be the allele for cystic fibrosis. The genotype of Charles would be Cc as he had a diseased child with his first wife. The genotype of Elaine can be either CC or Ccbecause her parents did not have the disease, but her brother had CF.

As a result, the woman has 1/3 chance of being CC as her parents were not diseased. However, she has a 2/3 chance of being a carrier (Cc) for the trait as her brother died of CF.

The probability of having a diseased child

The father is a carrier (Cc) for CF. If the mother is also a carrier (Cc) for CF, then the chances that Charles and Elaine would have a diseased child is ¼ (1/2 × ½). However, if the mother is normal (CC), there are zero chances that the child would have CF.

This means the probability of the child being diseased depends on the genotype of the mother. Therefore, the probability that the child has CF can be calculated as$(\frac{2}{3} \times \frac{1}{4}) + (\frac{1}{3} \times 0) = \frac{1}{6}$

Thus, the probability that the child will have CF is 1/6.