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Question
In a certain race, there are three boys X,Y, Z. The winning probability of X is twice than Y and the winning probability of Y is twice than Z. If P(X) + P(Y) + P(Z) = 1, then find the winning probability of each girl.
Solution
Let the probability of winning of girls Z be 'X'
∴ P(z) = x
∴ P(y) = 2P(z) = 2x
∴ P(x) = 2 P(y) = 4x
According to given condition
P(x) + P(y) + P(z) = 1
∴ 4x + 2x + x = 1
∴ 7x = 1
∴ x = `1/7`
∴ P(x) = 4x = `4 xx 1/7 = 4/7`
∴ P(y) = 2x = `2xx1/7 = 2/7`
∴ P(z) = x = `1/7`
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