Question

If $A, B, C$ are three mutually exclusive and exhaustive events of an experiment such that $P(A)= 2P (B) = 3P (C)$, then $P (B)$ is equal to

• A. $\frac{1}{11}$
• B. $\frac{2}{11}$
• C. $\frac{3}{11}$
• D. $\frac{4}{11}$

Answer 1

Answer: (C)

Given, $P(A)=2 P(B)=3 P(C)$
$\Rightarrow P ( C )=2 / 3 P ( B )$
Since $A , B , C$ are three mutually exclusive and exhaustive events
$\therefore P(A)+P(B)+P(C)=1$
$\Rightarrow P ( B )=3 / 11$