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

The correct option is B $\frac{1}{3}$

A and B are two Mutually Exclusive events so $P(A\cap B)=0$
$A\cup B=S\Rightarrow P(A\cup B)=1$
$P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)$
$1=P\left(A\right)+2P\left(A\right)-0$
$P\left(A\right)=\frac{1}{3}$