Question

Let two events $A$ and $B$ are such that, probability of occurrence of only $A$ is $\frac{3}{10}$ and probability of occurrence of $B$ is $\frac{3}{5}.$ Then the probability of occurrence of any of two events is

• A. $\frac{3}{10}$
• B. $\frac{1}{2}$
• C. $\frac{3}{5}$
• D. $\frac{9}{10}$

Answer 1

The correct option is D $\frac{9}{10}$

Given : $P(A\cap B^c)=\frac{3}{10},P\left(B\right)=\frac{3}{5}$
So,
$P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)=P(A\cap B^c)+P\left(B\right)=\frac{9}{10}[\because P(A)-P(A\cap B)=P(\text{only}A\left)\right]$