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A man and his wife appeared for an interview for the two vacancies. If the probability of husband's selection is 13\frac{1}{3} and the probability of wife's selection is 15\frac{1}{5}, then the probability that none of them will be selected?

Solution

✅ Correct Option: 2

The probability of husband's selection is 13\frac{1}{3} and the probability of wife's selection is 15\frac{1}{5}.

To find the probability that none of them will be selected, we need the probability that both get rejected.

Probability that husband is not selected:

P(husband not selected)=1−13P(\text{husband not selected}) = 1 - \frac{1}{3}

=23= \frac{2}{3}

Probability that wife is not selected:

P(wife not selected)=1−15P(\text{wife not selected}) = 1 - \frac{1}{5}

=45= \frac{4}{5}


Since the selections are independent events, the probability that both are not selected is the product of their individual probabilities.

Probability that none of them will be selected:

P(none selected)=P(husband not selected)×P(wife not selected)P(\text{none selected}) = P(\text{husband not selected}) \times P(\text{wife not selected})

=23×45= \frac{2}{3} \times \frac{4}{5}

=815= \frac{8}{15}


Therefore, the probability that none of them will be selected is 815\frac{8}{15}.

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