Question

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

• A. $\frac{27}{25}$
• B. $\frac{27}{50}$
• C. $\frac{7}{25}$
• D. $\frac{14}{25}$

Answer 1

Answer: (B)

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