Question

Two dice are tossed. Find whether the following two events A and B are independent. A = {(x, y) : x + y = 11}, B = {(x, y): x ≠ 5}, where (x, y) denote a typical sample point.

Answer 1

Total possible outcomes = 36 

A = {(x, y) : x + y = 11}, B = {(x, y) : x ≠ 5} 

A = {(5, 6), (6, 5)} 

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

A ∩ B = {(6, 5)}

So A and B are not independent.