Concept:
ABO blood grouping is controlled by:
\[
\boxed{
I^A,\ I^B,\ i
}
\]
where:
• \(I^A\) produces antigen A
• \(I^B\) produces antigen B
• \(i\) produces no antigen
Step 1: Write genotype of parents.
Man with blood group AB:
\[
\boxed{
I^A I^B
}
\]
Woman with blood group O:
\[
\boxed{
ii
}
\]
Step 2: Determine gametes.
Gametes produced by father:
\[
I^A,\ I^B
\]
Gametes produced by mother:
\[
i,\ i
\]
Step 3: Prepare genetic combinations.
Possible offspring combinations:
\[
I^A \times i \rightarrow I^A i
\]
\[
I^B \times i \rightarrow I^B i
\]
Thus children can have:
• Blood group A
• Blood group B
Step 4: Calculate proportions.
Probability:
\[
50% \rightarrow \text{Blood group A}
\]
\[
50% \rightarrow \text{Blood group B}
\]
Thus:
\[
\boxed{
\text{Half A and half B}
}
\]
Step 5: Choose correct answer.
Hence correct option is:
\[
\boxed{(3)}
\]
Final Conclusion:
Cross:
\[
I^A I^B \times ii
\]
produces:
\[
50% \text{ A group} \quad \text{and} \quad 50% \text{ B group}
\]
Hence correct answer is:
\[
\boxed{(3)}
\]