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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 probabilities of their winning.
Solution
Let the probability of winning of C be x
p(c) = x
P(B) = 2x [Given]
P(A) = 4x [Given]
P(A) + P(B) + P(C) = 1 [Given]
4x + 2x + x = 1
7x = 1
x = `1/7`
P(A) = 4x
= 4 `(1/7)`
=`4/7`
P(B) = 2x
= `2 (1/7)`
= `2/7`
P(C) = x
= `1/7`
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