Three students A, B and C are running a race. A and B have the same probability of winning and each is twice…
Three students A, B and C are running a race. A and 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 equal to (assuming there are no ties)
$\frac{2}{5}$
$\frac{3}{5}$
$\frac{3}{7}$
$\frac{2}{7}$
Solution
Let winning probability of C be P(C) = p
$\begin{aligned} & \therefore \quad P(A)=P(B)=2 p \\ & \because \quad P(A)+P(B)+P(C)=1 \\ & 2 p+2 p+p=1 \\ & \Rightarrow \quad 5 p=1 \\ & p=1 / 5 \\ & \end{aligned}$
$\therefore$ Probability that $B$ or $C$ win $=P(B)+P(C)$
$=2 p+p[\because B$ and $C$ are mutually exclusive events $]$
$
=3 p=\frac{3}{5}
$