Q218 / 270 · NDA 2020 · Mathematics

A husband and wife appear in an interview for two vacancies for the same post. The probability of the husband's selection is $\frac{1}{7}$ and that of wife's selection is $\frac{1}{5}$. If the events are independent, then the probability of which one of the following is $\frac{11}{35}$ ?

  • Correct answer
    A
    At least one of them will be selected
  • B
    Only one of them will be selected
  • C
    None of them will be selected
  • D
    Both of them will be selected

Solution

Probability for Husband's selection $P(H)=\frac{1}{7}$ Probability when Husband is not selection $P\left(H^{\prime}\right)=1-\frac{1}{7}=\frac{6}{7}$ Probability for wife's selection $P(W)=\frac{1}{5}$ Probability when Wife is not selected $P\left(W^{\prime}\right)=1-\frac{1}{5}=\frac{4}{5}$ As both are independent event. So, probability for atleast one of them will be selected $=P(H) P\left(W^{\prime}\right)+P\left(H^{\prime}\right) P(W)$ $=\frac{1}{7} \times \frac{4}{5}+\frac{6}{7} \times \frac{1}{5}=\frac{11}{35}$

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

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