Let E and F be events with P (E)= 3/5, P (F) = 3/10 and P (E ∩ F) = 1/5. Are E and F independent?

A fair coin and an unbiased die are tossed. Let A be the event ‘head appears on the coin’ and B be the event ‘3 on the die’. Check whether A and B are independent events or not.

A die marked 1, 2, 3 in red and 4, 5, 6 in green is tossed. Let A be the event, ‘the number is even,’ and B be the event, ‘the number is red’. Are A and B independent?

Given that the events A and B are such that P(A) = 1/2, P (A ∪ B) = 3/5 and P(B) = p. Find p if they are (i) mutually exclusive (ii) independent.

Let A and B be independent events with P (A) = 0.3 and P(B) = 0.4. Find

(i) P(A ∩ B) (ii) P(A ∪ B)

(iii) P (A|B) (iv) P (B|A)