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If the man is heterozygous but the woman is homozygous recessive, what are the chances that their child will be homozygous dominant?

If a father is heterozygous and the mother is homozygous recessive, the chance of having a homozygous dominant child is zero. Each parent gives one allele of the gene to the child, so that the child ends up with two copies--one from dad, and one from mom. The father is heterozygous, so he has an equal chance of donating either the dominant gene (let's call it G) or the recessive gene (g) to the child....




If a father is heterozygous and the mother is homozygous recessive, the chance of having a homozygous dominant child is zero.
Each parent gives one allele of the gene to the child, so that the child ends up with two copies--one from dad, and one from mom. The father is heterozygous, so he has an equal chance of donating either the dominant gene (let's call it G) or the recessive gene (g) to the child. But the mother's genotype is gg. She can only give a recessive gene to the child. To be homozygous dominant, as your question asks, the child would have to have the genotype GG. But as mom has ONLY "g" to give, the child cannot be homozygous dominant.
The child in this scenario can SHOW the dominant trait; that is, have the phenotype for the dominant trait. This only requires one copy of the dominant trait, which the children will receive from dad half the time.
In sum, children from this mother and father will have the genotype Gg half the time, and gg half the time. On average, half of the couple's children will show the dominant trait (Gg), and the half that receive gg will show the recessive form of the trait.

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