Statistics And Probability Question 53
Question: A man and a woman appear in an interview for two vacancies in the same post. The probability of man?s selection is ¼ and that of the woman?s selection is 1/3. Then the probability that none of them will be selected is.
Options:
A) $ \frac{1}{2} $
B) $ \frac{3}{4} $
C) $ \frac{2}{3} $
D) $ \frac{2}{5} $
Show Answer
Answer:
Correct Answer: A
Solution:
- [a] Let M be the events that a man will be selected and W the events that a woman will be selected. Then, $ P(M)=\frac{1}{4},,so,P(M)=1-\frac{1}{4}=\frac{3}{4} $ $ P(W)=\frac{1}{3},,so,P(W)=\frac{2}{3} $ Clearly $ M $ and $ W $ are independent events. So, $ P(M\cap W)=P(M)\times P(W)=\frac{3}{4}\times \frac{2}{3}=\frac{1}{2}. $
BETA
