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?

Answer 1

Let the probability of winning of horse C is $x$.

then probability of winning B is $2x$ and probability of winning A is $4x$.

Also total probability of winning is $1$.

So $P\left(A\right)+P\left(B\right)+P\left(C\right)=1$

$\Rightarrow x+2x+4x=1\Rightarrow x=\frac{1}{7}$

Hence probability of winning of horses A,B, and C are $\frac{4}{7},\frac{2}{7}$ and $\frac{1}{7}$ respectively.