Q10 of 105 Page 546

Events A and B are such that P (A) = 1/2, P(B) = 7/12 and P(not A or not B) = 1/4. State whether A and B are independent ?

Given: P (A) =, P(B) =and P(not A or not B) = 1/4

⇒ P (A’∪ B’) = 1/4


⇒ P (A ∩ B)’ = 1/4


⇒ 1 - P (A ∩ B) = 1/4


⇒ P (A ∩ B) = 1 - 1/4


⇒ P (A ∩ B) = 3/4 ..(1)


And P(A) . P(B) = ..(2)


From (1) and (2) P (A ∩ B) ≠ P(A) . P(B)


Therefore, A and B are not independent events.


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