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 the complement of the event A. Then, the events A and B are ?
A
Independent but not equally likely
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B
Independent and equally likely
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C
Mutually exclusive and independent
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D
Equally likely but not independent
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Solution
The correct option is A Independent but not equally likely Given, P(¯¯¯¯¯¯¯¯¯¯¯¯¯¯A∪B)=16;P(A∩B)=14;P(¯A)=14 ∴P(A∪B)=1−P(¯¯¯¯¯¯¯¯¯¯¯¯¯¯A∪B)=1−16=56
And P(A)=1−P(¯A)=1−14=34 ∴P(A∪B)=P(A)+P(B)−P(A∩B) ⇒56=34+P(B)−14 ⇒P(B)=13⇒ A and B are not equally likely P(A∩B)=P(A).P(B)=14
So, events A and B are independent.