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).