Let A and B be two events such that P(A∪B¯)=16, P(A∩B)=14 and P(A)=14 where A¯ stands for complement of event A. Then events A and B are

We have,P(A∪B¯)=14,P(A∩B)=14P(A¯)=14⇒P(A)=1−14=34∴ P(A∪B¯)=1−P(A∪B)=1−[P(A)+P(B)−P(A∩B)]⇒16=1−34−P(B)+14⇒ P(B)=1−12−16=6−3−16=26=13Since P(A∩B)=P(A)P(B) and P(A)≠P(B), therefore A and B are independent but not equally likely.