Probability Question 176
Question: If two events A and B are such that $ P(A^{c})=0.3,P(B)=0.4 $ and $ P(AB^{c})=0.5, $ then $ P[B/(A\cup B^{c})] $ is equal to
[IIT 1994]
Options:
A) $ \frac{1}{2} $
B) $ \frac{1}{3} $
C) $ \frac{1}{4} $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
$ P[B/(A\cup B^{c})]=\frac{P(B\cap (A\cup B^{c}))}{P(A\cup B^{c})} $
$ =\frac{P(A\cap B)}{P(A)+P(B^{c})-P(A\cap B^{c})} $
$ =\frac{P(A)-P(A\cap B^{c})}{P(A)+P(B^{c})-P(A\cap B^{c})} $
$ =\frac{0.7-0.5}{0.8}=\frac{1}{4} $ .
BETA
