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 probability of winning?
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Answer 1

Answer

Let the probability of winning of horse C is xx.

then probability of winning B is 2x2x and probability of winning A is 4x4x.

Also total probability of winning is 11.

So P(A)+P(B)+P(C)=1P(A)+P(B)+P(C)=1

\Rightarrow x+2x+4x=1\Rightarrow x=\dfrac{1}{7}⇒x+2x+4x=1⇒x=

7

1

Hence probability of winning of horses A,B, and C are \dfrac{4}{7}, \dfrac{2}{7}

7

4

,

7

2

and \dfrac{1}{7}

7

1

respectively.