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Q.

The horses A, B and C run a race. If the probability of $A^{' s}$ win is twice that of B and the probability of $B^{' s}$ win the thrice that of C then the probabilities of their winning are

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a

$\frac{6}{10}, \frac{3}{10}, \frac{1}{10}$

b

$\frac{4}{7}, \frac{2}{7}, \frac{1}{10}$

c

$\frac{5}{10}, \frac{2}{10}, \frac{3}{10}$

d

$\frac{1}{2}, \frac{1}{3}, \frac{1}{4}$

answer is A.

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Detailed Solution

$\begin{array}{l} P (A) = 2 P (B) = 3 P (C) \\ L e t P (C) = x \\ P (B) = 3 x, P (A) = 2 (3 x) = 6 x \\ P (A \cup B \cup C) = 1 \\ P (A) + P (B) + P (C) = 1 \\ 6 x + 3 x + x = 1 \\ \Rightarrow x = \frac{1}{10} \\ P (A) = \frac{6}{10}, P (B) = \frac{3}{10}, P (C) = \frac{1}{10} \end{array}$

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