# hw1 - p and tails with probability q = 1-p We toss the coin...

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Homework # 1, Due Tuesday, January 17 In Problems 1-3 express your answer in terms of factorials. 1. Problem. A poker hand consists of 5 cards chosen from the standard set of 52 cards. What is the probability that a random poker hand is a) a Fush? (all 5 cards are of the same suit.) b) two pairs? (the cards have denominations a, a, b, b, c , where a, b and c are all distinct.) 2. Problem. A bridge hand consists of 13 cards chosen from the standard set of 52 cards. What is the probability that a random bridge hand is void in at least one suit? 3. Problem. A coin turns up heads with probability
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Unformatted text preview: p and tails with probability q = 1-p . We toss the coin n times. What is the probability that the number of heads and the number of tails are equal? 4. Let A and B be events with probabilities P ( A ) = 3 / 4 and P ( B ) = 1 / 3. ±ind the smallest and the largest possible values of P ( A ∩ B ) and of P ( A ∪ B ). 5. Let A 1 and A 2 be events. Prove that P ( A 1 ∩ A 2 ) ≥ P ( A 1 ) + P ( A 2 )-1. Prove that in general P ( A 1 ∩ . . . ∩ A n ) ≥ n s i =1 P ( A i )-( n-1) for events A 1 , . . . , A n in a probability space. 1...
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