Q4 of 23 Page 1

Attempt of the following sub questions:
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.

P(A) denotes winning probability of A


P(B) denotes winning probability of B


P(C) denotes winning probability of C


Let P(C) = x …(i)


By given


P(B) = 2 × P(C)


⇒ P(B) = 2x …(ii)


and


P(A) = 2 × P(B)


⇒ P(A) = 2 × 2x


⇒ P(A) = 4x …(iii)


P(A) + P(B) + P(C) =1 …given


⇒ 4x + 2x + x = 1 …using (i) (ii) and (iii)


⇒ 7x = 1


∴ x =


Therefore, substituting value of x in equation (i), (ii) and (iii)


P(C) = x =


P(B) = 2x =


P(A) = 4x =


Hence winning probabilities of A, B and C are , and respectively


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