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A man and a woman appear in an interview...

A man and a woman appear in an interview for two vacancies in the same post. The probability of mans selection of 1/4 and that the womans selection is 1/3. What is the probability that none of them will be selected?

Text Solution

Verified by Experts

The correct Answer is:
`1//2`
Let `E_(1)` be the events that man will be selected and `E_(2)` the events that woman will be selected. Then,
`P(E_(1))=1/4soP(barE_(1))=1-1/4=3/4`
`P(E_(2))=1/3,soP(barE_(2))=1-1/3=2/3`
Clearly `E_(1)and E_(2)` are independent evets. So,
`P(barE_(1)nnbarE_(2))=P(barE_(1))xxP(barE_(2))=3/4xx2/ 3=1/2`
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