Question

Let $A,B$ be two events such that probability of occurrence of any one is $\frac{3}{5},$ probability of occurrence of only $B$ is $\frac{2}{10}.$ Then the probability of occurrence of $A$ is

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

Answer 1

The correct option is C $\frac{2}{5}$

Given : $P(A\cup B)=\frac{3}{5},P\left(B\right)-P(A\cap B)=\frac{2}{10}$
$\Rightarrow P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)\Rightarrow P\left(A\right)=\frac{3}{5}-\frac{2}{10}=\frac{2}{5}$