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Question
Three horses A, B, C are in the race. A is twice as likely to win as B and B is twice as likely to win as C. What are their respective probabilities of winning?
Solution
Given that A is twice as likely to win as B.
Therefore, A : B = 2 : 1
or A : B = 4 : 2 …….(1)
Also given that B is twice as likely to win as C.
Therefore, B : C = 2 : 1 ………(2)
From (1) and (2),
A : B : C = 4 : 2 : 1
∴ A = 4k, B = 2k, C = 1
where C is a constant of proportionality.
Probability of A wining is `(4"k")/(7"K") = 4/7`
Probability of B wining is `(2"k")/(7"k") = 2/7`
Probability of C wining is `(1"k")/(7"k") = 1/7`
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