Question

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.

Answer 1

The sample space of this experiment will be as follows.

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)}

A = Head appears on the coin; B = Number 3 appears on the die.

(A ∩ B) = {(H, 3}}

and  n(S) = 12, n(A) = 6, n(B) = 2

and n(A ∩ B) = 1

∴ P(A) = `(n(A))/(n(S)) = 6/12 = 1/2`,

P(B) = `(n(B))/(n(S)) = 2/12 = 1/6`

and P(A ∩ B) = `(n(A ∩ B))/(n(S))`

= `1/12`

= `1/2 . 1/6`

= P(A) . P(B)

Therefore, events A and B are independent.