Question

Karen and Steve each have a sibling with sickle cell disease. Neither Karen nor Steve nor any of their parents have the disease, and none of them have been tested to see if they carry the sickle-cell allele. Based on this incomplete information, calculate the probability that if this couple has a child, the child will have sickle-cell disease.

Short answer

The parents of Karen and Steve are the carriers of sickle cell disease, so their siblings develop sickle cell disease. The probability of Karen and Steve’s child acquiring sickle-cell disease is 1/9.

Step-by-step solution

Inheritance 

The possibility of developing a disease through the transfer of defective genes is known as inheritance. Inheritance is the important property that is analyzed in the development of diseases such as sickle cell anemia.

Sickle cell anemia is a disease condition in which the red blood cells get affected and result in anemia.

Diagrammatic representation of the pattern of inheritance

If N is the dominant allele and n is the recessive allele for the trait. The probability is designed to find the possibility of inheritance of disease in the child from the given conditions.

The genotype of Karen and Steve’s parents must be Nn as they are the carrier for the trait. The genotype of the siblings must be nn because sickle-cell anemia is an autosomal recessive disorder.

Probability that makes the child develop the disease

The parent of Karen and Steve does have the gene, which denotes that the parents are the carrier, and the probability of Karen being the carrier of this disease is 2/3.

The likelihood of Steve acquiring the disease is similar to Karen. Karen and Steve are marrying to give birth to a child. The chance of a child acquiring this disease is ¼ from the alleles shared by Karen and Steve.

The overall probability of the child to develop the sickle-cell allele is calculated as follows: $\frac{2}{3}\times \frac{2}{3}\times \frac{1}{4}=\frac{1}{9}$