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If two dice are rolled simultaneously, find the probability of the following events. 

i. The sum of the digits on the upper faces is at least 10. 

ii. The sum of the digits on the upper faces is 33. 

iii. The digit on the first die is greater than the digit on second die.

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Best answer

Sample space, 

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

i. Let A be the event that the sum of the digits on the upper faces is at least 10.

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

ii. Let B be the event that the sum of the digits on the upper faces is 33. 

The sum of the digits on the upper faces can be maximum 12.

∴ Event B is an impossible event.

iii. Let C be the event that the digit on the first die is greater than the digit on the 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),

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