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Question
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.
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`
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