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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