2. Discuss the concepts of mutually exclusive events and independent events. List several examples of each type

Question:

2. Discuss the concepts of mutually exclusive events and independent events. List several examples of each type of event from everyday life.

(a) If A and B are mutually exclusive events, does it follow that A and B cannot be independent events? Give an example to demonstrate your answer.

Hint: Discuss an election where only one person can win the election. Let A be the event that party A’s candidate wins, and let B be the event that party B’s candidate wins. Does the outcome of one event determine the outcome of the other event? Are A and B mutually exclusive events?

(b) Discuss the conditions under which P1A and B2 5 P1A2 # P1B2 is true. Under what conditions is this not true?

(c) Discuss the conditions under which P1A or B2 5 P1A2 1 P1B2 is true.

Under what conditions is this not true?

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