# 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? - Algebra

Sum

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

Let P(C) be x.

Probability of horse B winning the race is twice as likely as C.

∴ P(B) = 2 × P(C)

= 2x

Probability of horse A winning the race is twice as likely as B.

P(A) = 2 × P(B)

= 2 × 2x

= 4x

The total probability is 1.

∴ P(A) + P(B) + P(C) = 1

∴ 4x + 2x + x = 1

∴ 7x = 1

∴ x = 1/7

∴ P(C) = x

= 1/7

P(B) = 2x

= 2 xx 1/7

= 2/7

P(A) = 4x

= 4 xx 1/7

= 4/7

∴ P(A) = 4/7

P(B) = 2/7

P(C) = 1/7

Concept: Probability - A Theoretical Approach
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