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Three students A, B, C are running a race, A, B have the same probability of winning and each is twice likely to win as C then the probability that B (or) C wins is

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$\frac{3}{5}$

$\frac{3}{7}$

$\frac{2}{7}$

$\frac{2}{5}$

answer is B.

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Detailed Solution

$P (C) = x P (A) = P (B) = 2 x$
A,B,C mutually exclusive events
$P (A \cup B \cup C) = 1 P (A) + P (B) + P (C) = 1 2 x + 2 x + x = 1 \Rightarrow x = \frac{1}{5} P (B \cup C) = P (B) + P (C) = 3 x = \frac{3}{5}$

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