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In a certain race, there are three boys A, B, C. The winning probability of A is twice than B and the winning probability of B is twice than C. If P(A) + P(B) + P(C) = 1, then find the probability of win for each boy.

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#### Solution

Given: P(A) = 2P(B) and P(B) = 2P(C)

∴ P(A) = 2[2P(C)] = 4P(C)

Now, P(A) + P(B) + P(C) = 1

∴ 4P(C) + 2P(C) + P(C) = 1

∴ 7P(C) = 1

∴P(C)= `1/7`

∴P(A) = 4P(C)= `4*1/7=4/7` and P(B) = 2P(C) = `2*1/7=2/7`

Concept: Basic Ideas of Probability

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