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?

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#### 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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