4.18 Probability rules. For each of the following situations, state the probability rule or rules that you would use and apply it or them. Write a sentence explaining how the situation illustrates the use of the probability rules.

1. (a) The probability of event A is 0.417. What is the probability that event A does not occur?

2. (b) A coin is tossed four times. The probability of zero heads is 1/16 and the probability of zero tails is 1/16. What is the probability that all four tosses result in the same outcome?

3. (c) Refer to part (b). What is the probability that there is at least one head and at least one tail?

4. (d) The probability of event A is 0.4 and the probability of event B is 0.8. Events A and B are disjoint. Can this happen?

5. (e) Event A is very rare. Its probability is −0.04. Can this happen?