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A, B, C are three horses participating in a race. The Probability of horse A to win the race is twice that of horse B and probability of horse B to win is twice that of horse $\mathrm{C}$. Then the probabilities of horses A, B and C to win the race are respectively
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The correct answer is:
$\frac{4}{7}, \frac{2}{7}, \frac{1}{7}$
Let the probability of $\mathrm{A}, \mathrm{B}, \mathrm{C}$ winning are $a, b, c$ respectively.
Then, $a+b+c=1$ ...(i)
Given that, $a=2 b \& b=2 c$
$\therefore c=\frac{b}{2}$
From $\mathrm{eq}^{\mathrm{n}}(\mathrm{i}) \Rightarrow 2 b+b+\frac{b}{2}=1 \Rightarrow b=\frac{2}{7}$ $a=2 b=\frac{4}{7}$ and $c=\frac{b}{2}=\frac{1}{7}$
So, the probability of horses A, B \& C to win are $\frac{4}{7}, \frac{2}{7}, \frac{1}{7}$ respectively.
Then, $a+b+c=1$ ...(i)
Given that, $a=2 b \& b=2 c$
$\therefore c=\frac{b}{2}$
From $\mathrm{eq}^{\mathrm{n}}(\mathrm{i}) \Rightarrow 2 b+b+\frac{b}{2}=1 \Rightarrow b=\frac{2}{7}$ $a=2 b=\frac{4}{7}$ and $c=\frac{b}{2}=\frac{1}{7}$
So, the probability of horses A, B \& C to win are $\frac{4}{7}, \frac{2}{7}, \frac{1}{7}$ respectively.
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