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1. Suppose that events A, B, and C are independent.

(a) Use a Venn diagram to find an expression for P ( A U B u C) that does not make use of a complemen t

(b) Find an e,cpression for P( A U 8 U C) thal does make use of a complement

2. A fair coin is tossed four times. What is the probability that the n umber of heads appearing on the first two tosses is equal to the number of heads appearing on the second two Ls?

3. Suppose that two cards are drawn from a standard 52-card poker deck. Let A be the event that both are either a jack, queen, king, or ace of hearts, and let B be the even t that both are aces. Are A and B independent? Note: There are 1.,326 equally-likely ways to draw two cards from a poker deck.

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