Human blood type is controlled by three different alleles: P, P,and i. The F^A and P^B are codominant, while the i allele is recessive. A man with blood type A has a son with blood type B and a daughter with blood type AB. What are all the possible genotypes of the biological mother?

To determine the possible genotypes of the biological mother, we need to consider the blood types and the inheritance patterns of the alleles involved.<br /><br />The man has blood type \( A \), which means his genotype could be either \( I^{A}I^{A} \) or \( I^{A}i \).<br /><br />The son has blood type \( B \), which means his genotype must be \( I^{B}i \). Since the father cannot provide an \( I^{B} \) allele, the mother must have provided the \( I^{B} \) allele.<br /><br />The daughter has blood type \( AB \), which means her genotype is \( I^{A}I^{B} \). The father can provide the \( I^{A} \) allele, so the mother must have provided the \( I^{B} \) allele.<br /><br />Given these conditions, the mother must have at least one \( I^{B} \) allele. Therefore, the possible genotypes for the mother are:<br /><br />1. \( I^{B}I^{B} \)<br />2. \( I^{B}i \)<br />3. \( I^{A}I^{B} \)<br /><br />These genotypes would allow the mother to pass on the necessary alleles to produce a son with blood type \( B \) and a daughter with blood type \( AB \).