Q4 of 23 Page 1

Attempt any two of the following subquestions:

Three horses A, B and C are in race, A is twice as likely to win as B and B is twice as likely to win as C. What are their probabilities of winning?

Let the probability of winning of horse X is denoted by P(X)

Let P(C) = p


Given P(B) = 2×P(B) = 2p


Also, P(A) = 2×P(A) = 2×2p = 4p


Sum of all probabilities = 1


P(A) + P(B) + P(C) = 1


⇒ 4p + 2p + p = 1


⇒ 7p = 1


⇒ p = 0.143


Therefore, P(A) = 4×p = 4×0.143 = = 0.572


P(B) = 2× p = 2×0.143 = 0.286


P(C) = p = 0.143


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