### JEE Main On 16 April 2018 Question 13

##### Question: Let A, B and C be three events, which are pair-wise independence and $ \bar{E} $ denotes the complement of an event E. $ P(A\cap B\cap C)=0 $ and $ P(C)>0, $ then $ P[(\bar{A}\cap \bar{B}|C)] $ is equal to [JEE Main 16-4-2018]

#### Options:

A) $ P(A+P(\bar{B}) $

B) $ P(\bar{A})-P(\bar{B}) $

C) $ P(\bar{A})-P(B) $

D) $ P(\bar{A})+P(\bar{B}) $

## Show Answer

#### Answer:

Correct Answer: C

#### Solution:

We need find $ P(\bar{A}\cap \bar{B}\cap |C)= $

shaded portions in Venn Diagram $ =P(\bar{A}\cap \bar{B}\cap |C)=\frac{P(\bar{A}\cap \bar{B}\cap C)}{P(C)} $

$ =\frac{P(C)-P(A\cap C-P(B\cap C)}{P(C)} $ $ =-\frac{P(A).P(C)-P(B).P(C)}{P(C)} $

$ =1-P(A)-P(B) $ $ =P(\bar{A})-P(B) $