# 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. - Algebra

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

Concept: Basic Ideas of Probability
Is there an error in this question or solution?