Question

In Homo sapiens, cataracts in the eyes and fragility of the bones are caused by dominant alleles that assort independently. A man with cataracts and normal bones marries a woman without cataracts but with fragile bones. The man's father had normal eyes and the woman's father had normal bones. What is the probability that the first child of this couple will have cataracts but not fragile bones?

Answer 1

The probability that the first child of a man with cataracts and a woman with fragile bones will have cataracts but not fragile bones is 25%.

Step-by-step explanation:

In Homo sapiens, the condition of having cataracts is caused by a dominant allele, while the condition of having fragile bones is also caused by a different dominant allele. These two alleles assort independently. Given that the man has cataracts and normal bones, his genotype could be Ccbb, because his father had normal eyes, indicating the man must have one recessive allele for non-cataracts. The woman, not having cataracts but having fragile bones, and her father having normal bones, could be ccBb.

The probability of their first child having cataracts but not fragile bones (Cbcb) would be calculated as follows: Each parent can pass on one allele from each pair - the man can pass on either a C (for cataracts) or a c (for no cataracts), and a b (for no fragile bones); the woman can pass on a c (for no cataracts) and either a B (for fragile bones) or b (for no fragile bones). The probability of the child having cataracts (C from father and c from mother) and not having fragile bones (b from father and b from mother) is 1/2 (for C) × 1/2 (for b from the mother), which is 1/4, or a 25% probability.