Probability Question 320
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:
Let M be the events that man will be selected and W the events that woman will be selected.
Then, $ P(M)=\frac{1}{4},soP(M)=1-\frac{1}{4}=\frac{3}{4} $
$ P(W)=\frac{1}{3},soP(W)=\frac{2}{3} $ Clearly $ M_1 $ 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
