Q77 / 160 · AP EAMCET 2019 (22 Apr Shift 1) · Mathematics

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
    \(\frac{27}{25}\)
  • Correct answer
    B
    \(\frac{27}{50}\)
  • C
    \(\frac{7}{25}\)
  • D
    \(\frac{14}{25}\)

Solution

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

Hence, the correct answer is option: 'B'.

Relevant Questions