Question

$A$, $B$, $C$ are three horses in a race. The probability of $A$ to win the race is twice that of $B$ and probability of $B$ is twice that of $C$. What are the probabilities of $A$, $B$ and $C$ to win the race?

Answer 1

Let the probability of $A,B,C$ winning are $a,b,c$ respectively

Then $a+b+c=1$

In question given $a=2b$

$b=2c$

Hence $c=\frac{b}{2}$

So $a+b+c=1$

$2b+b+\frac{b}{2}=1$

$\frac{7b}{2}=1$

$b=\frac{2}{7}$

$a=2b=\frac{4}{7}$

$c=\frac{b}{2}=\frac{1}{7}$

So $P_A=a=\frac{4}{7}$

$P_B=b=\frac{2}{7}$

$P_C=c=\frac{1}{7}$