Question

In a swimming race 3 swimmers compete . The probability of A and B wining is same and twice that of C. What is the probability that B or C wins. Assuming no two finish the race at the same time.

• A. $\frac{2}{10}$
• B. $\frac{1}{5}$
• C. $\frac{3}{5}$
• D. $\frac{8}{10}$

Answer 1

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

Let, probability of C winning be $P\left(C\right)=p$

Probability of A winnig $P\left(A\right)=2p$

Probability of B winnig $P\left(B\right)=2p$

We know that, sum of probabilities of all the events is 1.
$\therefore P\left(A\right)+P\left(B\right)+P\left(C\right)=12p+2p+p=15p=1\therefore p=\frac{1}{5}$
Since B and C are mutually exclusive events,
$P\left(BUC\right)=P\left(B\right)+P\left(C\right)=\frac{2}{5}+\frac{1}{5}=\frac{3}{5}$