Basic Theorems of Probability

In exercise 24 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 or independent or neither?

b) If you examine two people, are the events that the first is Type A and the second Type B disjoint or independent or neither?

c) Can disjoint events ever be independent? Explain.

d) Write the definition of disjoint events and the definition of independent events. How do these definitions tell you the answers to parts a, b, and c?