Question

A,B,C aree three horses in a race. The probability of A to win the race is twice that of B and probability of B is twice that of C. What are the probabilities of A B and C to win the race

Answer 1

Let A,B,C are three horses win the race representing as events A, B, C respectively.

$\mathrm \red{Given} \\ \\ P(A) = 2 P(B) \\\ \\P(B) = 2 P(C)$

$\\ \mathrm{P(A) = 2 P(B) = 2 [2 P(C)] \: = \: 4P(C)} \\ \\ \mathrm{We \: know \: that; \: P(A) + P(B) + P(C) = 1} \\ \\ \mathrm{4P(C) + 2P(C) + P(C) = 1} \\ \\ \mathrm{7P(C) \: = 1} \\ \\ \mathrm{P(C) \: = \: \frac{1}{7} }$

$\mathrm \red{Then : }$

$\mathrm{P(A) \: = 4 P(C) \: = \: 4 \times \frac{1}{7} = \frac{4}{7} } \\ \\ \mathrm{P(B) = 2P(C) \: = \: 2 \times \frac{1}{7} = \frac{2}{7} } \\ \\ \boxed{ \mathrm \red{ \therefore \: P(A) \: = \: \frac{4}{7} , \: P(B) \: = \frac{2}{7}, \: P(C) \: = \: \frac{1}{7} }}$