Question
If A and B are two events such that P(A) = 12 and P(B) = 23, then
Answer: Option D
:
D
We have P(A∪B)≥ max. {P(A),P(B)}=23
P(A∩B)≤ min.{P(A),P(B)}=12
and P(A∩B)=P(A)+P(B)−P(A∪B)≥P(A)+P(B)−1=16
⇒16≤P(A∩B)≤12
P(A′∩B)=P(B)−P(A∩B)
Hence 23−12≤P(A′∩B)≤23−16
⇒16≤P(A′∩B)≤12
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D
We have P(A∪B)≥ max. {P(A),P(B)}=23
P(A∩B)≤ min.{P(A),P(B)}=12
and P(A∩B)=P(A)+P(B)−P(A∪B)≥P(A)+P(B)−1=16
⇒16≤P(A∩B)≤12
P(A′∩B)=P(B)−P(A∩B)
Hence 23−12≤P(A′∩B)≤23−16
⇒16≤P(A′∩B)≤12
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