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problems10-sol - MATH S-104 Lecture 10 In-class Problem...

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MATH S-104 Lecture 10 In-class Problem Solutions July 23, 2009 Problem 1 * : a) Find the probability of rolling at least one six when a die is rolled four times. The number of ways that a non-six can be rolled four times is 5 4 . The total number of ways that one die can be rolled four times is 6 4 . Thus, the probability that no six is rolled is 5 4 6 4 , so the probability that at least one six is rolled is 1 - 5 4 6 4 = 6 4 - 5 4 6 4 = 671 1296 = 0 . 517 b) Find the probability that at least one six or at least one one is rolled when a die is rolled four times. Let S 1 be the set of 4-roll instances with at least one one, and let S 6 be the set of 4-roll instances with at least one six. We are interested in ± S 1 S 6 ± , the size of the set with at least one one or at least one six. It is easier to compute the set of 4-roll sequences with no ones or sixes: ± ( S 1 S 6 = 4 4 Since there are 6 4 total 4-roll instances, the probability of getting an instance that does have either a one or a six is: ± S 1 S 2 ± = 6

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problems10-sol - MATH S-104 Lecture 10 In-class Problem...

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