If two dice are rolled simultaneously, find the probability: (1) sum of the digits on the upper faces is at least 10 (2) the sum is 33 (3) the digit on the first die is greater than the digit on second die.

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

(1) The sum of the digits on the upper faces is at least 10.
(2) The sum of the digits on the upper faces is 33.
(3) The digit on the first die is greater than the digit on second die.

Doubtly Asked 24 Oct 2026 Save WhatsApp Report

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Answer: (1) 1/6 (2) 0 (3) 5/12

n(S) = 36.

(1) Sum at least 10: A = {(4,6), (5,5), (6,4), (5,6), (6,5), (6,6)}, n(A) = 6.

\[ P(A) = \frac{6}{36} = \frac{1}{6} \]

(2) The greatest possible sum is 12, so a sum of 33 is impossible: n(B) = 0, P(B) = 0.

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

n(C) = 1 + 2 + 3 + 4 + 5 = 15.

\[ P(C) = \frac{15}{36} = \frac{5}{12} \]

Doubtly AI · 24 Oct 2026 AI-verified · Oct 2026 Report

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If two dice are rolled simultaneously, find the probability: (1) sum of the digits on the upper faces is at least 10 (2) the sum is 33 (3) the digit on the first die is greater than the digit on second die.

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