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.
Given two independent events A and B such that P(A) = 0.3, P(B) = 0.6.
Find
(i) P(A and B) (ii) P(A and not B)
(iii) P(A or B) (iv) P(neither A nor B)
(view answer)