Question

Two dice are thrown together. Let A be the event ‘getting 6 on the first die’ and B be the event ‘getting 2 on the second die’. Are the events A and B independent?

Answer 1

A = {(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

B = {(1, 2), (2, 2), (3, 2), (4, 2), (5, 2), (6, 2)}

A ∩ B = {(6, 2)}

P(A) = `6/36 = 1/6`

P(B) = `1/6`

P(A ∩ B) = `1/36`

Events A and B will be independent if

P(A ∩ B) = P(A) P(B)

i.e., L.H.S = P(A ∩ B) = `1/36`

R.H.S = P(A) P(B) = `1/6 xx 1/6 = 1/36`

Hence, A and B are independent.