Two persons A and B appear in an interview for two vacancies. If the probabilities of their selections are 1/4 and 1/6 respectively, then the…

Two persons A and B appear in an interview for two vacancies.

Probability A is selected $= \frac{1}{4}$=41​

Probability B is selected $= \frac{1}{6}$=61​

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The probability that A is not selected:

$$P(\text{A not selected}) = 1 - \frac{1}{4}$$P(A not selected)=1−41​

$$= \frac{3}{4}$$=43​

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The probability that B is not selected:

$$P(\text{B not selected}) = 1 - \frac{1}{6}$$P(B not selected)=1−61​

$$= \frac{5}{6}$$=65​

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Since A's selection and B's selection are independent events, the probability that both are not selected:

$$P(\text{None selected}) = P(\text{A not selected}) \times P(\text{B not selected})$$P(None selected)=P(A not selected)×P(B not selected)

$$= \frac{3}{4} \times \frac{5}{6}$$=43​×65​

$$= \frac{15}{24}$$=2415​

$$= \frac{5}{8}$$=85​

Therefore, the probability that none of them is selected $= \frac{5}{8}$=85​