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### Three People Toss a Coin

```
Date: 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/
```
Associated Topics:
High School Probability

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