Attempt any two sub-questions from the following:

Two dice are thrown, find the probability of getting:
(a) The sum of the numbers on their upper faces is at least 10.
(b) The sum of the number on their upper faces kin divisible by 5.
(c) The number on the upper face of the first die is greater than the number on the upper face of the second die.

Two dice are thrown

∴S = {(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),

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

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

∴ n (S) = 36

(a) Let A be the event that sum of numbers on their upper faces is divisible by 9

A = {(4, 6), (5, 5), (5, 6), (6, 4), (6, 5), (6, 6)}

n (A) = 6

P (A) = n (A)/n (S)

∴ P (A) = 6/36

∴ P (A) = 1/6

(b) Let B be the event that sum of number on their upper faces is at the most 3.

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

n (B) = 6

P (B) = n (B)/n (S)

∴ P (B) = 6/36

∴ P (B) = 1/6

(c) Let C be the event that number on the upper face of the first die is greater than the number on the upper face of second die.

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

n (C) = 15

P (C) = n (C)/n (S)

∴ P (C) = 15/36

∴ P (C) = 5/12