Probability Question 151
Question: If A and B are events such that $ P(A\cup B)=3/4, $
$ P(A\cap B)=1/4, $
$ P(\bar{A})=2/3, $ then $ P(\bar{A}\cap B) $ is
[AIEEE 2002]
Options:
A) $ \frac{5}{12} $
B) $ \frac{3}{8} $
C) $ \frac{5}{8} $
D) $ \frac{1}{4} $
Show Answer
Answer:
Correct Answer: A
Solution:
$ P(A\cup B)=\frac{3}{4}, $
$ P(A\cap B)=\frac{1}{4} $
$ P(\bar{A})=\frac{2}{3}\Rightarrow $ $ P(A)=\frac{1}{3} $
$ \therefore $ $ P(A\cap B)=P(A)+P(B)-P(A\cup B) $
$ \frac{1}{4}=\frac{1}{3}+P(B)-\frac{3}{4} $
Therefore $ P(B)=\frac{2}{3} $ $ P(\bar{A}\cap B) $ = $ P(B)-P(A\cap B) $
$ =\frac{2}{3}-\frac{1}{4}=\frac{8-3}{12}=\frac{5}{12}. $
BETA
