A man and a woman are each heterozygous carriers of an autosomal recessive mutation of a disorder that is fatal in infancy. They both want to have multiple children, but they are concerned about the risk of the disorder appearing in one or more of their children. In separate calculations, determine the probabilities of the couple having five children with 0, 1, 2, 3, 4, and all 5 children being affected by the disorder.

Key Concepts

Autosomal Recessive Inheritance

Autosomal recessive inheritance occurs when a disorder is caused by mutations in genes located on autosomes, and two copies of the mutated gene (one from each parent) are necessary for the disorder to manifest. In this case, both parents are heterozygous carriers, meaning they each have one normal allele and one mutated allele. Their children have a 25% chance of inheriting two mutated alleles and thus being affected by the disorder.

Punnett Square

A Punnett square is a diagram used to predict the genetic outcomes of a cross between two individuals. For this couple, a 2x2 Punnett square can illustrate the possible combinations of alleles their children might inherit. The results show that there is a 25% probability of a child being affected by the disorder, a 50% chance of being a carrier, and a 25% chance of being unaffected.

Binomial Probability

Binomial probability is a statistical method used to determine the likelihood of a specific number of successes in a fixed number of trials, given a constant probability of success. In this scenario, the couple can use the binomial formula to calculate the probabilities of having 0, 1, 2, 3, 4, or 5 affected children out of 5 total, using the probability of 0.25 for each child being affected.