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NDA 2020
Exam
NDA
Year
2020
Subject
Mathematics
Chapter
Probability

NDA 2020 · Mathematics · Probability

A husband and wife appear in an interview for two vacancies for the...

A husband and wife appear in an interview for two vacancies for the same post. The probability of the husband's selection is 17\frac{1}{7} and that of wife's selection is 15\frac{1}{5}. If the events are independent, then the probability of which one of the following is 1135\frac{11}{35} ?

Options

  1. AAt least one of them will be selected
  2. BOnly one of them will be selected
  3. CNone of them will be selected
  4. DBoth of them will be selected

Correct answer

A. At least one of them will be selected

Step-by-step solution

Probability for Husband's selection P(H)=17P(H)=\frac{1}{7} Probability when Husband is not selection P(H′)=1−17=67P\left(H^{\prime}\right)=1-\frac{1}{7}=\frac{6}{7} Probability for wife's selection P(W)=15P(W)=\frac{1}{5} Probability when Wife is not selected P(W′)=1−15=45P\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(W′)+P(H′)P(W)=17×45+67×15=1135=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}
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