Question

An experiment yields $3$ mutually exclusive and exhaustive events $A,B$ and $C$ $.$ If $P\left(A\right)=2P\left(\right.B\left.\right)=3P\left(C\right),$ then $P\left(A\right)$ is equal to

• A. $\frac{1}{11}$
• B. $\frac{2}{11}$
• C. $\frac{3}{11}$
• D. $\frac{6}{11}$

Answer 1

Answer: (D)

Given, events $A, \, B$ and $C$ are mutually exclusive and exhaustive, hence $P\left(A \cup B \cup C\right)=1$
$\Rightarrow \, P\left(A\right)+P\left(B\right)+P\left(C\right)=1$
$\Rightarrow P\left(A\right)+\frac{1}{2}P\left(A\right)+\frac{1}{3}P\left(A\right)=1$
$\Rightarrow \, \frac{11}{6}P\left(A\right)=1$
$\Rightarrow P\left(A\right)=\frac{6}{11}$