1. (10 points) Let A, B and C be random events. Indicate True or False for each

Question

1. (10 points) Let A, B and C be random events. Indicate True or False for each of the following. (a) T (b) T (c) T If A and B are disjoint, then P(AUB) 0. If A and C are independent, then B and C are also independent. Assume that A and B are disjoint, and A and C are independent. Also, P(A) = 0.5, P(B) = 0.3, and PC) = 0.3. With this information, P(AUB) = 0.5 + 0.3-0.15. Using the information from the previous item, we can say that P(Anc) 0.15. Using the information from the item (c), P(Ac) = P(B F F F (d) T e) T F F

Explanation / Answer

a) False. Because P(A U B) = P(A) + P(B) . for disjoint events

b) False

c) False. P(A U B) = 0.5 + 0.3

d) True.

e) False. P(Ac) = 1 - P(A)

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