The probability of occurrence of an event is $\frac{2}{5}$ and the probability of non-occurrence of another event is $\frac{3}{10}$. If these events are independent, then the probability that only one of the two events occur is

Question

Aicharya · Accepted Answer

Given, $P(A)=\frac{2}{5}$ $\begin{aligned} & \therefore \quad P(A)^{\prime}=1-P(A)=1-\frac{2}{5}=\frac{3}{5} \ & \text { and } \ & P(B)^{\prime}=\frac{3}{10} \ & \therefore \quad P(B)=1-P(B)^{\prime}=1-\frac{3}{10}=\frac{7}{10} \ & \text { Required probability }=P(A) P(B)^{\prime}+P(A)^{\prime} P(B) \ & =\frac{2}{5} \times \frac{3}{10}+\frac{3}{5} \times \frac{7}{10} \ & =\frac{6}{50}+\frac{21}{50}=\frac{27}{50} \end{aligned}$

The probability of occurrence of an event is \(\frac{2}{5}\) and the probability of non-occurrence of…

Solution