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.

Answer 1

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`