Probability Question 267
Question: $ P(A\cup B)=P(A\cap B) $ if and only if the relation between $ P(A) $ and $ P(B) $ is
[IIT 1985]
Options:
A) $ P(A)=P(\bar{A}) $
B) $ P(A\cap B)=P(A’\cap B’) $
C) $ P(A)=P(B) $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
$ P(A)=P(B) $
As this gives $ P(A\cup B)=P(A)+P(B)-P(A\cap B) $ or $ P(A)=2P(A)-P(A) $
$ \Rightarrow P(A\cup B)=P(A\cap B). $
BETA
