If A and B are two events such that P(A) = 12 and P(B) = 23, then
Options:
A .  
P(A∪B)≥23
B .  
16≤P(A′∩B)≤12
C .  
16≤P(A∩B)≤12
D .  
All of the above
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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