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.