Probability Question 244
Question: If A and B are any two events, then the probability that exactly one of them occur is
[BIT Ranchi 1990; IIT 1984; RPET 1995, 2002; MP PET 2004]
Options:
A) $ P(A)+P(B)-P(A\cap B) $
B) $ P(A)+P(B)-2P(A\cap B) $
C) $ P(A)+P(B)-P(A\cup B) $
D) $ P(A)+P(B)-2P(A\cup B) $
Show Answer
Answer:
Correct Answer: B
Solution:
Required probability $ =A $ occurs and $ B $ does not occur or B occurs and $ A $ does not occur $ =P(A\cap \bar{B})+P(\bar{A}\cap B) $
$ =P(A)-P(A\cap B)+P(B)-P(A\cap B) $
$ =P(A)+P(B)-2P(A\cap B) $ .
BETA
