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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
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`
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