Given: A fair coin and an unbiased die are tossed.

We know that the sample space S:

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 be the event ‘head appears on the coin:

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

⇒ P(A) =

Now, Let B be the event 3 on the die:

⇒ B = {(H,3), (T,3)}

As, A ∩ B = {(H,3)}

⇒ P(A ∩ B) = ..(1)

And P(A) . P(B) = ..(2)

From (1) and (2) P (A ∩ B) = P(A) . P(B)

Therefore, A and B are independent events.