Question

A fair coin and an unbiased dice are tossed. Let A be the event ‘head appears on the coin’ and B be the event 3 on dice. Check whether A and B are independent events or not.

Answer 1

When a coin is thrown, head or tail will occur.

∴ Probability of getting head P(A) = \(\frac{1}{2}\).

when a dice is tossed 1, 2, 3, 4, 5, 6 one of them will appear.

∴ Probability of getting 3 = P(B) = \(\frac{1}{6}\).

When a coin and a dice are tossed, total number of cases are

H1, H2, H3, H4, H5, H6

T1, T2, T3, T4, T5, T6

Head and 3 will occur only in 1 way.

∴ Probability of getting head and 3 = \(\frac{1}{12}\).

i.e; P(A ∩ B) = \(\frac{1}{12}\).

∴ P(A) × P(B) = \(\frac{1}{2}\) × \(\frac{1}{6}\) = \(\frac{1}{12}\)

∴ P(A ∩ B) = P(A) × P(B)

⇒ Events A and B are independent