Sickle cell anemia is an inherited blood disease that occurs primarily in blacks. In the United States, about 15 of every 10,000 black children have sickle cell anemia. The red blood cells of an affected person are abnormal; the result is severe chronic anemia (inability to carry the required amount of oxygen), which causes headaches, shortness of breath, jaundice, increased risk of pneumococcal pneumonia and gallstones, and other severe problems. Sickle cell anemia occurs in children who inherit an abnormal type of hemoglobin, called hemoglobin S, from both parents. If hemoglobin S is inherited from only one parent, the person is said to have sickle cell trait and is generally free from symptoms. There is a 50% chance that a person who has sickle cell trait will pass hemoglobin S to an offspring.
a. Obtain the probability that a child of two people who have sickle cell trait will have sickle cell anemia.
b. If two people who have sickle cell trait have five children, determine the probability that at least one of the children will have sickle cell anemia.
c. If two people who have sickle cell trait have five children, find the probability distribution of the number of those children who will have sickle cell anemia.
d. Construct a probability histogram for the probability distribution in part (c).
e. If two people who have sickle cell trait have five children, how many can they expect will have sickle cell anemia?