Should You Play?Date: 08/07/97 at 22:29:16 From: Connie Subject: Face card probability A game consists of three cuts with a deck of 52 cards. You win $1 if a face card turns up on at least one cut, but you lose $1 if a face card does not turn up. Should you play? Why? Thanks, Connie Date: 08/08/97 at 05:03:24 From: Doctor Anthony Subject: Re: Face card probability A game is considered fair if the expectation is zero. That is, if in a long series of games you would expect to break even. The definition of 'expectation' if x1 occurs with probability p1, x2 occurs with probability p2, and so on, is: E(x) = p1.x1 + p2.x2 + p3.x3 + ...... + pn.xn To find the probabilities of at least one face card in 3 trials, consider instead the probability of no face card in 3 trials, and subtract this probability from 1. Probability of no face card in three trials = (9/13)^3 = .331816 Probability of at least one face card in 3 trials = 1 - (9/13)^3 = 0.66818 Your expectation = 1 x .66818 - 1 x .331816 = 0.33637 With a positive expectation you should certainly play. -Doctor Anthony, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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