#### Question

Three horses A, B and C are in a 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?

#### Solution

Pr(A) = 2Pr(B), and Pr(B) = 2Pr(C)

Hence, Pr(A) = 4Pr(C)

But Pr(A) + Pr(B) + Pr(C) = 1

Consequently, 4Pr(C) + 2Pr(C) + 1Pr(C) = 1

So, Pr(C) = 1/7

Since Pr(B) = 2Pr(C)

Pr(B) = 2/7

and since Pr(A) = 4Pr(C)

Pr(A) = 4/7

Is there an error in this question or solution?

#### APPEARS IN

Solution Three horses A, B and C are in a 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? Concept: Probability - A Theoretical Approach.