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 \(\frac{4k}{7k}=\frac{4}{7}\)

Probability of B wining is \(\frac{2k}{7k}=\frac{2}{7}\)

Probability of C wining is \(\frac{k}{7k}=\frac{1}{7}\)