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stat hw1 - accept Problem 5(p.52#25 A pair of dice is...

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Problem 1: (p.16 #18) A committee of 7, consisting of 2 Republicans, 2 Democrats, and 3 Independents, is to be chosen from a group of 5 Republicans, 6 Democrats, and 4 Independents. How many committees are possible? Problem 2: (p.17 #28) If 8 new teachers are to be divided among 4 schools, how many divisions are possible? What if each school must receive 2 teachers? Problem 3: (p.18 #8) Prove that Hint : Consider a group of n men and m women. How many groups of size r are possible? Problem 4: (p.51 #9) A retail establishment accepts either the American Express or the VISA credit card. A total of 24% of its customers carry an American Express card, 61% carry a VISA card, and 11% carry both cards. What percentage of its customers carry a credit card that the establishment will
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Unformatted text preview: accept? Problem 5: (p.52 #25) A pair of dice is rolled until a sum of either 5 or 7 appears. Find the probability that a 5 occurs first. Hint: Let E n denote the event that a 5 occurs on the n th roll and no 5 or 7 occurs on the first n – 1 rolls. Compute P ( E n ) and argue that P ( E n ) is the desired probability. Problem 6: (p.53 #39) There are 5 hotels in a certain town. If 3 people check into hotels a day, what is the probability that they each check into a different hotel? What assumptions are you making? Problem 7: (p.55 #9) Suppose that an experiment is performed n times. For any event E of the sample space, let n ( E ) denote the number of times that event E occurs and define f ( E )/ n . Show that f ( . ) satisfies Axioms 1, 2, and 3....
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