Two dice are thrown at the same time. Find the probability that the sum of the two numbers appearing on the top of the dice is :
(i) 0
(ii) 12
(iii) less than 12
(iv) less than or equal to 12

Question

Two dice are thrown at the same time. Find the probability that the sum of the two numbers appearing on the top of the dice is : (i) 0 (ii) 12 (iii) less than 12 (iv) less than or equal to 12

KnowledgeBoat · Accepted Answer

(i) Total number of possible outcomes = 36 (i.e., (1, 1), (1, 2), (1, 3), (1, 4), .................(6, 4), (6, 5), (6, 6)) Number of favourable outcomes (where the sum of the two numbers appearing on the top of the dice is 0) = 0 P(where the sum of the two numbers appearing on the top of the dice is 0) = = = 0 Hence, the probability of the sum of the two numbers on the top of the dice being 0 is 0. (ii) Total number of possible outcomes = 36 (i.e., (1, 1), (1, 2), (1, 3), (1, 4), .................(6, 4), (6, 5), (6, 6)) Number of favourable outcomes (where the sum of the two numbers appearing on the top of the dice is 12) = 1 ((6, 6)) P(where the sum of the two numbers appearing on the top of the dice is 12) = = Hence, the probability of the sum of the two numbers on the top of the dice being 12 is . (iii) Total number of possible outcomes = 36 (i.e., (1, 1), (1, 2), (1, 3), (1, 4), .................(6, 4), (6, 5), (6, 6)) Number of favourable outcomes (where the sum of the two numbers appearing on the top of the dice is less than 12) = 35 ((1, 1), (1, 2), (1, 3), ..............(6, 5)) P(where the sum of the two numbers appearing on the top of the dice is less than 12) = = Hence, the probability of the sum of the two numbers on the top of the dice being less than 12 is . (iv) Total number of possible outcomes = 36 (i.e., (1, 1), (1, 2), (1, 3), (1, 4), .................(6, 4), (6, 5), (6, 6)) Number of favourable outcomes (where the sum of the two numbers appearing on the top of the dice is less than or equal to 12) = 36 ((1, 1), (1, 2), (1, 3), ..............(6, 5), (6, 6)) P(where the sum of the two numbers appearing on the top of the dice is less than or equal to 12) = = = 1 Hence, the probability of the sum of the two numbers on the top of the dice being less than or equal to 12 is 1.

Mathematics

Two dice are thrown at the same time. Find the probability that the sum of the two numbers appearing on the top of the dice is :
(i) 0
(ii) 12
(iii) less than 12
(iv) less than or equal to 12

Probability

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