Question: Disjoint or independent? In Exercise you calculated probabilities involving various blood types. Some of your answers depended on the assumption that the outcomes described were disjoint; that is, they could not both happen at the same time. Other answers depended on the assumption that the events were independent; that is, the occurrence of one of them doesn't affect the probability of the other. Do you understand the difference between disjoint and independent?
a) If you examine one person, are the events that the person is Type A and that the person is Type B disjoint, independent, or neither?
b) If you examine two people, are the events that the first is Type A and the second Type B disjoint, independent, or neither?
c) Can disjoint events ever be independent? Explain.
Exercise: Blood. The American Red Cross says that about 45% of the U.S. population has Type O blood, 40% Type A, 11% Type B, and the rest Type AB.
a) Someone volunteers to give blood. What is the probability that this donor
1) has Type AB blood?
2) has Type A or Type B?
3) is not Type O?
b) Among four potential donors, what is the probability that
1) all are Type O?
2) no one is Type AB?
3) they are not all Type A?
4) at least one person is Type B?