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?

Answer 1

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`