Question

A dice, marked 1, 2, 3 in red and 4, 5, 6 in green is tossed. Let A be the event ‘number is even’ and B be the event ‘number is red’. Are A and B are independent?

Answer 1

Even numbers on dice are 2, 4, 6.

∴ Probability of getting an even number = P(A) = \(\frac{3}{6}\) = \(\frac{1}{2}\).

There are two colours on the dice viz. red and green.

Probability of getting red colour P(B) = \(\frac{1}{2}\).

Even number in red colour is 2.

∴ Probability of getting red colour and even number

P(A ∩ B) = \(\frac{1}{6}\)

P(A) P(B) = \(\frac{1}{2}\) × \(\frac{1}{2}\) = \(\frac{1}{4}\) ≠ \(\frac{1}{6}\) ≠ P(A ∩ B) = \(\frac{1}{6}\).

⇒ A and B are not independent.