Question
Question: A man and a woman appear in an interview for two vacancies in the same post. The probability of man'...
A man and a woman appear in an interview for two vacancies in the same post. The probability of man's selection is 1/4 and that of the woman's selection is 1/3. What is the probability that none of them will be selected
A
21
B
121
C
41
D
None of these
Answer
21
Explanation
Solution
Let E1 be the event that man will be selected and E2 the event that woman will be selected. Then
P(E1)=41 so P(Eˉ1)=1−41=43 and P(E2)=31
So P(Eˉ2)=32
Clearly E1 and E2 are independent events.
So, P(Eˉ1∩Eˉ2)=P(Eˉ1)×P(Eˉ2)=43×32=21 .