Probability Question 155
Question: If A and B are two events such that $ P(A)\ne 0 $ and $ P(B)\ne 1, $ then $ P( \frac{{\bar{A}}}{{\bar{B}}} )= $
[IIT 1982; RPET 1995, 2000; DCE 2000; UPSEAT 2001]
Options:
A) $ 1-P( \frac{A}{B} ) $
B) $ 1-P( \frac{{\bar{A}}}{B} ) $
C) $ \frac{1-P(A\cup B)}{P(\bar{B})} $
D) $ \frac{P(\bar{A})}{P(\bar{B})} $
Show Answer
Answer:
Correct Answer: C
Solution:
$ P( \frac{\overline{A}}{\overline{B}} )=\frac{P(\overline{A}\cap \overline{B})}{P(\bar{B})}=\frac{P(\overline{A\cup B})}{P(\bar{B})}=\frac{1-P(A\cup B)}{P(\bar{B})}. $
BETA
