NCERT Solutions
Class 12 Maths
Probability
Ex.13.2 Q.4
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.
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) = 
B: 3 on die
B = {(H, 3), (T, 3)}
=> P(B) = 
Now, A ∩ B = {(H, 3)}
P(A ∩ B) = 
P(A) * P(B) =
Therefore, A and B are independent events.