Final answer:
To determine the probability of Barbara's next son having hemophilia, we need to know her genotype. If she is a carrier, there is a 50 percent chance for each son to inherit hemophilia, as it is an X-linked recessive disorder.
Step-by-step explanation:
The probability that Barbara's next son will have hemophilia, an X-linked recessive disorder, is determined by her genotype. If Barbara is a carrier of the disorder, then her son has a 50 percent chance of being affected. Since hemophilia is a recessive condition, and it is X-linked, a male only needs one copy of the affected X chromosome to exhibit the disorder.
Females, on the other hand, must inherit two copies of the affected chromosome to manifest the disease. Since females have two X chromosomes, they can be carriers of the disorder without being affected by it. Therefore, without knowing the exact genotype of Barbara, it is not possible to determine the probability of her next son being hemophiliac.
Hemophilia is more common in males because they only need one mutated X chromosome to be affected, whereas females would need two. Because Barbara's first son has hemophilia, it implies that she has at least one affected X chromosome. If Barbara is a carrier (only one of her X chromosomes has the mutation), the chance of passing on the affected X chromosome to a son is 50 percent.