Question

Refer to Question 1 above. If the die were fair, determine whether or not the events A and B are independent.

Answer 1

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

∴ n(A) = 6 and n(S) = 6 × 6 = 36

So, P(A) = `("n"("A"))/("n"("S")) = 6/36 = 1/6`

And B = {(4, 6), (6, 4), (5, 5), (5, 6), (6, 5), (6, 6)}

n(B) = 6 and n(S) = 36

∴ P(B) = `("n"("B"))/("n"("S")) = 6/36 = 1/6`

A ∩ B = {(5, 5), (6, 6)}

∴ P(A ∩ B) = `2/36 = 1/18`

Therefore, if A and B are independent

Then P(A ∩ B) = P(A) . P(B)

⇒ `1/18 ≠ 1/6 xx 1/6`

⇒ `1/18 ≠ 1/36`

Hence, A and B are not independent events.