Question

In a swimming competition, only $3$ students $A,B$ and $C$ are taking part. The probability of $A^{\prime }s$ winning or the probability of $B^{\prime }s$ winning is three times the probability of ${}^{\prime }s$ winning. The probability of the event either $B$ or $C$ to win is

• A. $\frac{1}{7}$
• B. $\frac{2}{7}$
• C. $\frac{3}{7}$
• D. $\frac{4}{7}$

Answer 1

The correct option is D $\frac{4}{7}$

P (A) = P (B) = 3P(C) ...... (given)

we know that ,

P (A) + P (B) + P (C) = 1

3P(C) + 3P(C) + P(C) = 1

$P\left(C\right)=\frac{1}{7}$

$\therefore$ P(B) = 3P (c)$=\frac{3}{7}$

Probability that either =P(B) + P(C)

B or C wins $=\frac{3}{7}+\frac{1}{7}=\frac{4}{7}$