Question

In a certain race there are 3 boys A, B,C. The winning probability of A is twice than B and the winning probability of B is twice than C. If B is twice than C. If $P\left(A\right)+P\left(B\right)+P\left(C\right)=1$ then find the probability of each boy.

Answer 1

First of all assume that probability of winning of C is "X"

So according to the question probability of Winning of B will be $2X$

and then again the probability of winning of A will be$=2\times 2X=4X$

Also in this case of probability $X+2X+4X=1$

$\Rightarrow 7X=1$

$\Rightarrow X=\frac{1}{7}$

Which means the probability for $C$ will be $=\frac{1}{7}$

The the probability of winning of $B$ will be $=\frac{2}{7}$

And the winning of probability for $A$ will be $=4X=\frac{4}{7}$