If A and B be two events such that P(A) = 1/4, P (B) = 1/3 and P (A ∪ B) = 1/2, show that A and B are independent events.

A card is drawn form a pack of 52 cards so that each card is equally likely to be selected. In which of the following cases are the events A and N independent?

i. A=the card drawn is a king or queen, B=the card drawn is a queen or jack

ii. A=the card drawn is black, B=the card drawn is a king

iii. B=the card drawn is a spade, B=the card drawn in an ace

A coin is tossed three times. Let the events A,B and C be defined as follows:

A=first toss is head, B=second toss is head, and C= exactly two heads are tossed in a row.

Check the independence of (i) A and B

(ii) B and C

(iii) C and A

Given two independent events A and B such that P (A)=0.3 and P(B) = 0.6 Find

i. P (A B)

ii.

iv.

iv. P (A ∪ B)

v. P (A / B)

vi. P (B / A)

If P (not B) = 0.65, P (A ∪ B) = 0.85, and A and B are independent events, then find p (A).