Sickle-cell anemia is an inherited disease in which red blood cells are misshapen and sticky. Sickle cells tend to form clumps in blood vessels, inhibiting the flow of blood. Humans have two genes for sickle-cell anemia, either of which may be S for normal cells or s for sickle cells. A person with two copies of the s gene will have sickle-cell anemia. A person with one s gene and one S gene will not have the disease, but will be a carrier, which means that the s gene may be transmitted to the person's offspring. If two carriers have a child, the probability is 0.25 that the child will have the disease and 0.5 that the child will be a carrier. Outcomes among children are independent.
a. A mother and father who are both carriers have two children. What is the probability that neither child has the disease?
b. What is the probability that both children are carriers?
c. If neither child has the disease, what is the probability that both are carriers?
d. A woman who is the child of two carriers has a child by a man who is a carrier. What is the probability that this child has the disease?