Three People Toss a CoinDate: 03/22/2002 at 03:36:27 From: George Corston Subject: Probability Three people (A, B, C) each toss a coin in order. The winner is the first to get a 'tail'. Expressed as fractions, what are their respective chances of winning? Date: 03/22/2002 at 07:05:13 From: Doctor Anthony Subject: Re: Probability If a = the probability that A wins, then he can win with probability 1/2 or get back to a with probability 1/8 (i.e. A, B and C all fail on their first turns). a = 1/2 + (1/8)a (7/8)a = 1/2 a = 8/14 = 4/7 Similarly if b = the probability that B wins, he can win on the first turn with probability 1/4 (i.e. A loses, B wins) or he can get back to b with probability 1/8. b = 1/4 + (1/8)b (7/8)b = 1/4 b = 2/7 and finally c = 1/7 So the probabilities are, respectively, 4/7, 2/7, and 1/7. - Doctor Anthony, The Math Forum http://mathforum.org/dr.math/ |
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