31. Assume that we have two events, A and B, that are mutually exclusive. Assume further that we know P(A)  .30 and P(B)  .40.

a. What is P(A  B)?

b. What is P(A  B)?

c. A student in statistics argues that the concepts of mutually exclusive events and independent events are really the same, and that if events are mutually exclusive they must be independent. Do you agree with this statement? Use the probability information in this problem to justify your answer.

d. What general conclusion would you make about mutually exclusive and independent events given the results of this problem?