At one gene locus in humans there are 2 alleles: one for curly hair and another for straight hair. Neither allele is dominant, and heterozygous individuals have wavy hair. At a second gene locus, 3 alleles control ABO blood type. The alleles at these 2 gene loci assort independently. A man with straight hair and A blood has children with a woman with wavy hair and B blood. Their first child has straight hair and O blood. If their second child is a boy with straight hair, what is the probability that he has A blood? (Express your answer as a percentage. Enter the number only without the percent sign. For example, enter 100% as 100 and enter 12.5% as 12.5.)
Question
At one gene locus in humans there are 2 alleles: one for curly hair and another for straight hair. Neither allele is dominant, and heterozygous individuals have wavy hair. At a second gene locus, 3 alleles control ABO blood type. The alleles at these 2 gene loci assort independently. A man with straight hair and A blood has children with a woman with wavy hair and B blood. Their first child has straight hair and O blood. If their second child is a boy with straight hair, what is the probability that he has A blood? (Express your answer as a percentage. Enter the number only without the percent sign. For example, enter 100% as 100 and enter 12.5% as 12.5.)
Solution
To answer this question, we need to understand the genetics behind the traits.
For the hair trait, the man has straight hair, so his genotype must be SS (where S represents the straight hair allele). The woman has wavy hair, which means she is heterozygous (SC, where C represents the curly hair allele).
For the blood type, the man has A blood, so his genotype could be either AA or AO (where A and O represent the A and O blood type alleles, respectively). The woman has B blood, so her genotype could be either BB or BO.
The first child has straight hair and O blood, which means the man must have AO genotype and the woman must have BO genotype.
Now, for the second child who has straight hair, he must have received the S allele from both parents. The probability of this happening is 1, because the man can only pass on the S allele and the woman has a 1/2 chance of passing on the S allele.
For the blood type, the boy could either have A or O blood. He can only receive the A allele from his father and the O allele from his mother. The probability of him receiving the A allele from his father is 1/2 and the probability of him receiving the O allele from his mother is 1/2.
Therefore, the probability that the boy has A blood is 1/2 * 1/2 = 1/4 = 25%.
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