hw1-extra - arrest Joe.) This continues at 1/8 hour before...

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AMS 311 (Fall, 2010) Joe Mitchell PROBABILITY THEORY Homework Set # 1 Due at the beginning of class on Thursday, September 16, 2010 Reminder: Show your reasoning! OPTIONAL EXTRA CREDIT CHALLENGE: Joe is throwing a New Year’s Eve Party. He invites his numerous (in±nite!) collection of friends, who show up as couples (2 people at a time). The ±rst couple arrives at 11:30pm, 1/2 hour before midnight. The police are watching outside Joe’s house, and the instant a couple arrives to the party, they rush in and make a drug bust, arresting a random guest (among the 2) and hauling them o² to prison. The next couple arrives at 11:45pm, 1/4 hour before midnight. Again, the police instantaneously rush in and arrest a random person from among Joe’s 3 guests. (They never
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Unformatted text preview: arrest Joe.) This continues at 1/8 hour before midnight, 1/16 hour, etc. Each drug bust is done so quickly it takes no time at all. What is the probability that Joe celebrates with at least 10 guests at the stroke of midnight? [Hint: Suppose the guests are numbered 1 , 2 , 3 , . . . ; the rst couple to arrive is { 1 , 2 } , then next is { 3 , 4 } , etc. Let E n be the event that guest number 1 is still at the party after the rst n drug busts. Note that the event that guest 1 celebrates with Joe at the stroke of midnight is the event i n =1 E n . Now apply Proposition 6.1 (of section 2.6) to the events E n , n 1.]...
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This note was uploaded on 07/15/2011 for the course AMS 311 taught by Professor Tucker,a during the Spring '08 term at SUNY Stony Brook.

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