hw2assmt - can’t hear the chicken clucking each door is...

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Math 341 Homework #2 Due Friday February 10 Problems from Chapter 1 : 17, 25 Problems from Chapter 2 : 1, 7, 11, 14 Theoretical Problems from Chapter 2 : 1, 2, 7 Extra Problem : below. 1. Let’s Make a Deal Paradox. This paradox is related to a popular television show in the 1970’s. In the show, a contestant was given a choice of three doors of which one contained a prize, say an all-expense-paid trip to Tahiti. The other two doors contained gag gifts like a chicken or a donkey. After the contestant chose an initial door, the host of the show then opened one of the two unchosen doors to reveal the gag gift, and asked the contestant if he or she would like to switch to the other unchosen door. The question is should the contestant switch. Do the odds of winning increase by switching to the remaining door? To answer this question, assume that your original choice is completely random (you
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Unformatted text preview: can’t hear the chicken clucking, each door is equally likely to be chosen) and that the three doors are equally likely to hold the prize before the game begins: (a) Construct the sample space for the strategy always switch doors using a 4-tuple ( u,v,w,x ), where u is the door you initially choose, v is the door number that the host opens, w is the door you switch to and x indicates whether you win or lose. For the first 4-tuple, assume the prize is behind door #1. For the second 4-tuple, assume the prize is behind door #2, and so on. What are the probabilities of each of the possible outcomes? (b) Construct the sample space for the strategy never switch doors as above. What are the probabilities of each of the possible outcomes? (c) What are the odds of winning if you switch? What are the odds of winning if you don’t?...
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