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 4tuple ( 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 4tuple, assume the prize is behind door #1. For the second 4tuple, 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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 Spring '08
 SMITH
 Math, Game Theory, Probability theory, Door, Paul Newman

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