Question

If $A$ and $B$ are two mutually exclusive events in a sample space $S$ such that $P\left(B\right)=2P\left(A\right)$ and $A\cup B=S$ then $P\left(A\right)=$

• A. $\frac{1}{2}$
• B. $\frac{1}{3}$
• C. $\frac{1}{4}$
• D. $\frac{1}{5}$

Answer 1

Answer: (B)

$\frac{1}{3}$

Since the events are mutually exclusive we have $P\left(A\right)+P\left(B\right)=1$.

Here we have $P\left(B\right)=2P\left(A\right)⟹3P\left(A\right)=1$

ie $P\left(A\right)=\frac{1}{3}$

Option B gives the correct answer