Probability Question 265
Question: For two given events A and B, $ P(A\cap B)= $
[IIT 1988]
Options:
A) Not less than $ P(A)+P(B)-1 $
B) Not greater than $ P(A)+P(B) $
C) Equal to $ P(A)+P(B)-P(A\cup B) $
D) All of the above
Show Answer
Answer:
Correct Answer: D
Solution:
It is obvious. $∵P(A∪B)=P(A)+P(B)−P(A∩B) $
on rearranging we get $P(A∩B)=P(A)+P(B)−P(A∪B) $
Also $∵0≤P(A∪B)≤1⇒P(A)+P(B)−1≤P(A∩B)≤P(A)+P(B)$
Now if $P(A∩B)=P(A)+P(B)+P(A∩B)$ $⇒P(A)+P(B)=0$ which is not necessary for the events A and B
BETA
