10

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.

10

11

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)