Question

If $A$ and $B$ are two independent events such that $P\left(B\right)=0.4$ and $P\left(A\cup B\right)=0.6$ , then $P\left(A\cap B\right)=$

• A. $\frac{1}{3}$
• B. $\frac{2}{3}$
• C. $\frac{1}{5}$
• D. None of the above

Answer 1

Answer: (D)

We have,
$P(A\cup B)=P(A)+P(B)-P(A\cap B)$
$\Rightarrow 0.6=P(A)+0.4-P(A)\cdot P(B)$
[$\because A$ and $B$ are independent events]
$\Rightarrow P(A)-0.4\times P(A)=0.2$
$\Rightarrow P(A)=\frac{0.2}{0.6}=\frac{1}{3}$
Now, $P(A\cap B)=P(A)\cdot P(B)$
$=\frac{1}{3}\times 0.4=\frac{2}{15}$