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 bad B independent events or not. 

A and B are independent events.

if a fair coin and an unbiased die are tossed, then the sample space S is given by,

S= {(H, 1), (H, 2), (H, 3), (H, 4), (H, 5),(H, 6), (T, 1), (T, 2), (T, 3), (T, 4), (T, 5), (T, 6)} 

Let A: Head appears on the coin

A = {(H, 1), (H, 2), (H, 3), (H, 4), (H, 5),(H, 6)}

⇒ P(A) = 6/12 = 1/2

B : 3 on die = {(H, 3), (T, 3)}

P(B) = 2/12 = 1/6

So, A∩B = {(H, 3)}

P(A∩B) = 1/12

P(A). P(B) = (1/2)x (1/6) = 1/12 = P(A∩B)

Therefore, A and B are independent events.