Two dice are thrown. Find the probability of getting an odd number on the first die and a multiple of 3 on the other.
Consider the following events:
A = getting an odd number on first die
B = getting a multiple of 3 on the second die.
We have, A = {1, 3, 5} and B = {3, 6}
∴ P(A) = 3/6=1/2 and P(B) = 2/6 = 1/3
Now Required probability = P(A ∩ B) = P(A) P (B) = 1/2 × 1/3 = 1/6
[A and B are independent events]