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Unformatted text preview: Math 425 Section 008 Homework 5 Chapter 4, problems 14, 22(a), 30, 35, 36, 38, 41, 43, 48 Problem 14. Five distinct numbers are randomly distributed to players num bered 1 to 5. Whenever two players compare their numbers, the one with the higher one is declared the winner. Initially, player 1 and 2 compare their num bers; the winner then compares with player 3, and so on. Let X denote the number of times player 1 is a winner. Find P { X = i } , i = 0 , 1 ,..., 4 . Solution. Notice that X i if and only if player 1 has the card of highest rank among players 1 , 2 ,...i + 1. The probability of such an event is 1 i +1 . So P { X i } = 1 i + 1 , i = 0 , 1 ,..., 4 Now, p ( i ) = P { X = i } = P { X i }  P { X i + 1 } Hence, p (0) = 1 1 2 ; p (1) = 1 2 1 3 ; p (2) = 1 3 1 4 ; p (3) = 1 4 1 5 ; p (4) = 1 5 . Problem. 22(a) Suppose that two teams play a series of games that end when one of them has won i games. Suppose that each game played, is, indepedently, won by team A with probability...
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 Winter '08
 Buckingham
 Math, Probability

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