What is the overall probability that the man will produce an Ab gamete?

Only the AABb genotype can produce Ab gametes, and the expected probability of Ab gametes produced will be 1/2. Because the parent has an equal probability (50%) of having either genotype (AaBB or AABb), the final probability of the parent producing an Ab gamete is (1/2) × (1/2) = 1/4 = 0.25 = 25%.