A pair of dice is thrown. If the two numbers appearing on them are different, find the probability (i) the sum of the numbers is 6(ii) the sum of the numbers is 4 or less (iii) the sum of the number is 4.

A = Number appearing on two dice are different

B = The sum of the numbers on two dice is 6

C = The sum of the numbers on two dice is 4 or less

D = the sum of the numbers on two dice is 4

Clearly, A = 

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

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

C = {(1, 1) (1, 2), (2, 1) (1, 3) (3, 1) (2, 2)}

D = ((1, 3), (3, 1) (2, 2)}

A ∩ B = {(1, 5) (5, 1) (2, 4) (4, 2) A ∩ C ={(1, 2) (2, 1) (1, 3) (3, 1)} A ∩ D = {(1, 3) (3, 1)}

n  (A ∩ B) = 4, n (A ∩ C) = 4, n (A ∩ D) = 2 and n (A) = 30