Question

A die marked 1, 2, 3 in red and 4, 5, 6 in green is thrown. Let A be the event ‘Number appearing is odd’ and B be the event ‘Number appearing is green’.

Prove that the events A and B are not independent.

Answer 1

Given:

Red = 1, 2, 3

Green = 4, 5, 6

A = No. Apparing is odd 

A = {1, 3, 5}   ...[Event A (Odd)]

P(A) = `3/6 = 1/2`   

B = No. Appearing is B = {4, 5, 6}    ...[Event B Green]

P(B) = `3/6 = 1/2`

A∩B = {5}

P(A∩B) = `1/6`

P(A) × P(B) = `1/2 × 1/2`

= `1/4`

P(A∩B) ≠ P(A)P

∴ A & B are not independent.