4.96 Find and explain some probabilities.

1. (a) Can we have an event A that has negative probability? Explain your answer.

2. (b) Suppose P(A) = 0.3 and P(B) = 0.5. Explain what it means for A and B to be disjoint. Assuming that they are disjoint, find the probability that A or B occurs.

3. (c) Explain in your own words the meaning of the rule P(S) = 1.

4. (d) Consider an event A. What is the name for the event that A does not occur? If P(A) = 0.4, what is the probability that A does not occur?

5. (e) Suppose that A and B are independent and that P(A) = 0.8 and P(B) = 0.3. Explain the meaning of the event {A and B}, and find its probability.