Human blood groups are determined by the ABO gene, which has three alleles: \( I^A \), \( I^B \), and \( i \). The \( I^A \) and \( I^B \) alleles are codominant, while \( i \) is recessive. The genotypes for the blood groups are:
- Blood group AB: \( I^A I^B \)
- Blood group O: \( ii \)
The man with blood group AB has the genotype \( I^A I^B \), and the woman with blood group O has the genotype \( ii \). To find the probability of their child having blood group A, we use a Punnett square to determine the possible genotypes of their offspring.
The man (\( I^A I^B \)) can contribute either an \( I^A \) or an \( I^B \) allele. The woman (\( ii \)) can only contribute an \( i \) allele. The possible genotypes of the offspring are:
\[
\begin{array}{c|cc}
& I^A & I^B
\hline
i & I^A i & I^B i
\end{array}
\]
- \( I^A i \): Blood group A (since \( I^A \) is dominant over \( i \)).
- \( I^B i \): Blood group B (since \( I^B \) is dominant over \( i \)).
The possible blood groups of the offspring are:
- Blood group A (\( I^A i \)): 1 out of 2 possibilities.
- Blood group B (\( I^B i \)): 1 out of 2 possibilities.
Thus, the probability that their child will have blood group A is:
\[
\frac{1}{2} = 50\%
\]