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

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$\frac{27}{25}$

$\frac{14}{25}$

$\frac{7}{25}$

$\frac{27}{50}$

answer is B.

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Detailed Solution

A, B are two events $\begin{array}{rcl} P (A) & = & \frac{2}{5} P (B) = \frac{3}{10} \end{array}$

$P (A) = \frac{3}{5}, P (B) = \frac{7}{10}$

probability that only one of the two events occur =

$\begin{array}{rcl} P (A \cap B) + P (A \cap B) \\ = & \frac{2}{5} \times \frac{3}{10} + \frac{3}{5} \times \frac{7}{10} = \frac{27}{50} \end{array}$

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