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.

Verified step by step guidance

1. Identify the inheritance pattern: Sickle-cell disease is inherited in an autosomal recessive manner. This means that a person must inherit two copies of the sickle-cell allele (one from each parent) to express the disease.
2. Determine the genotype of the siblings with the disease: Since sickle-cell disease is autosomal recessive and the siblings have the disease, they must have the genotype ss (where 's' represents the sickle-cell allele).
3. Analyze the parents' genotypes: Since neither Karen's nor Steve's parents have the disease, but they have children who do, each parent must be a carrier of one sickle-cell allele. Therefore, each parent's genotype must be Ss (where 'S' represents the normal allele).
4. Calculate the probability of Karen and Steve being carriers: Since both sets of parents are carriers (Ss), Karen and Steve each have a 2/3 chance of being a carrier themselves, because the possible genotypes they could inherit are SS (1/4 chance) or Ss (3/4 chance), but we exclude SS as a possibility since we know they have a sibling with ss.
5. Determine the probability of their child having sickle-cell disease: If both Karen and Steve are carriers (each with a probability of 2/3), the probability that both pass the sickle-cell allele to their child is (2/3) * (2/3) * (1/4) = 1/9. This calculation comes from the probability that both are carriers multiplied by the probability that both pass on the sickle-cell allele (1/4, as each can pass on either S or s with equal probability).

Key Concepts

Sickle-Cell Disease Genetics

Sickle-cell disease is an autosomal recessive disorder caused by a mutation in the HBB gene, leading to abnormal hemoglobin. Individuals with two copies of the sickle-cell allele (homozygous recessive) exhibit the disease, while those with one copy (heterozygous) are carriers but do not show symptoms. Understanding this inheritance pattern is crucial for calculating the probability of offspring inheriting the disease.

Punnett Square

A Punnett square is a diagram used to predict the genetic makeup of offspring from two parents. It illustrates the possible combinations of alleles that can result from the mating of two individuals. By using a Punnett square, one can determine the likelihood of a child inheriting specific traits, such as sickle-cell disease, based on the genotypes of the parents.

Carrier Probability

In this scenario, since neither Karen nor Steve has sickle-cell disease, they could be carriers of the sickle-cell allele. The probability of them being carriers can be inferred from their siblings' conditions. If both siblings have sickle-cell disease, it suggests that both parents are likely carriers, which affects the probability of their child inheriting the disease. Understanding carrier status is essential for calculating the risk of the child having sickle-cell disease.