SOLUTION: A,B,C are three horses in a race. The probability of A to win the race is twice that of B, and the probability of B is twice that of C. What is the probability of A to loose the

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Question 1160575: A,B,C are three horses in a race. The probability of A to win the race is twice that of B, and the probability of B is twice that of C. What is the probability of A to loose the race? Give your answer to nearest 4 dp.
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
the probability of A winning the race is equal to p(a).
the probability of B winning the race is equal to p(b).
the probability of C winning the race is equal to p(c).
p(a) = 2 * p(b)
p(b) = 2 * p(c)
sum of all probabilities equals 1
therefore:
p(a) + p(b) + p(c) = 1
since p(a) = 2 * p(b), then:
2 * p(b) + p(b) + p(c) = 1
since 2 * p(b) = p(c), then:
2 * 2 * p(c) + 2 * p(c) + p(c) = 1
simplify to get:
4 * p(c) + 2 * p(c) + p(c) = 1
combine like terms to get:
7 * p(c) = 1
solve for p(c) to get:
p(c) = 1/7
p(b) = 2 * p(c) = 2/7
p(a) = 2 * p(b) = 4/7
1/7 + 2/7 + 4/7 = 1 which is the sum of all probabilties, as it should be.
the probability of A losing the race is 1 minus the probability of A winning the race = 1 - 4/7 = 3/7.
that's your solution.