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Interview selection probability

CMAT 2020 · Quantitative Techniques & Data Interpretation · Easy · Probability

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Brother and sister both appear for an interview. The probability of the selection of brother is 18\frac{1}{8} while the probability of rejection of sister is 45\frac{4}{5}. What is the probability that only one of them is selected ?

  1. A.

    1140\frac{11}{40}

  2. B.

    740\frac{7}{40}

  3. C.

    513\frac{5}{13}

  4. D.

    110\frac{1}{10}

Answer

A

Explanation

P(Brother selected)=18P(\text{Brother selected}) = \frac{1}{8}, P(Brother rejected)=78P(\text{Brother rejected}) = \frac{7}{8}. P(Sister rejected)=45P(\text{Sister rejected}) = \frac{4}{5}, P(Sister selected)=15P(\text{Sister selected}) = \frac{1}{5}.

P(Only one selected)=P(Brother selected)P(Sister rejected)+P(Brother rejected)P(Sister selected)P(\text{Only one selected}) = P(\text{Brother selected})P(\text{Sister rejected}) + P(\text{Brother rejected})P(\text{Sister selected}) =(18)(45)+(78)(15)=440+740=1140= \left(\frac{1}{8}\right)\left(\frac{4}{5}\right) + \left(\frac{7}{8}\right)\left(\frac{1}{5}\right) = \frac{4}{40} + \frac{7}{40} = \frac{11}{40}.

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