Question

Three athletes A, B and C participate in a race. Both A and B have the same probability of winning the race and each is twice as likely to win as C. The probability that B or C wins the race is

• A. $\frac{2}{3}$
• B. $\frac{3}{5}$
• C. $\frac{3}{4}$
• D. $\frac{13}{15}$

Answer 1

The correct option is B $\frac{3}{5}$

P(A) = P(B) = 2P (c) = x (say)
$\therefore P\left(A\right)+P\left(B\right)+P\left(C\right)=1\Rightarrow x=\frac{2}{5}P\left(A\right)=\frac{2}{5}=P\left(B\right),P\left(C\right)=\frac{1}{5}$
$\therefore$ The probability that B or C wins the race
$=P\left(B\right)+P\left(C\right)=\frac{2}{5}+\frac{1}{5}=\frac{3}{5}$