Q77 / 160 · AP EAMCET 2023 (17 May Shift 2) · Mathematics

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

  • Correct answer
    A
    $\frac{4}{7}, \frac{2}{7}, \frac{1}{7}$
  • B
    $\frac{1}{6}, \frac{2}{6}, \frac{5}{6}$
  • C
    $\frac{1}{4}, \frac{1}{2}, \frac{1}{7}$
  • D
    $\frac{4}{7}, \frac{3}{7}, \frac{1}{7}$

Solution

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.

Hence, the correct answer is option: 'A'.

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