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

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

Let A be the event where a head appears.

A = {1H2H3H4H5H6H}

Then P(A) = 612=12

Let B be the event that a 3 appears on the die.

B = {3H3T}

Then P(B) = 312=16

We can see that A ∩ B = {3H}

Therefore, P (A ∩ B) = 112

We know that if A and B are independant events, P(A∩B)=P(A)P(B)

⇒P(A)P(B)=12×16=112= P(A ∩ B).

Therefore A and B are independent events.