Judy and Sam are thinking of having children, but Sam's brother has galactosemia (a rare autosomal, recessive disease) and Judy's great-grandmother also had galactosemia. Judy has a sister who has three children, none of whom have galactosemia. What is the probability that Sam and Judy's first child will be a daughter with galactosemia?

If Judy is heterozygous for the trait then the probability that Sam and Judy's first child will be a daughter with galactosemia is 1/8

If Judy is homozygous dominant for the trait then the probability that Sam and Judy's first child will be a daughter with galactosemia is 0

Explanation:

Autosomal recessive traits appear only when a person inherits two alleles for the trait, in other words if they are homozygous recessive for the trait.

Let galactosemia=g and normal=G

We know that Judy's great-grandmother was affected, thus we know she was gg but because the disease is rare, Judy's great-grandfather was probably GG. Their children would all have been carriers or Gg who would have children with a partner that is GG. Thus there is a 50% chance that one of Judy's parents could be a carrier, therefore there is a 50% chance that Judy could be a carrier.

We also know that Sam's brother is affected, we then know that both Sam's parents are carriers (Gg x Gg), therefore Sam must also be a carrier if he is not affected.

The probability of having a daughter is 1/2.

If we assume Judy is a carrier of the disease and we know Sam is a carrier

Gg x Gg

they could yield: 1/4 GG, 1/2 Gg, 1/4 gg

∴ 1/4 x 1/2 = 1/8 probability of having a daughter with galactosemia

But if Judy is not a carrier

GG x Gg

they could yield: 1/2 GG, 1/2 Gg

∴ 0 x 1/2 = 0 probability of having a daughter with galactosemia