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When two six-sided dice are rolled, there are $36$36​ possible outcomes.a. Find the probability that the sum is not $4$4​ . Express your first answer as a fraction in simplest form, and round your percent answer to the nearest whole percent. or about $\%$%​b. Find the probability that the sum is greater than $5$5​ . Express your first answer as a fraction in simplest form, and round your percent answer to the nearest whole percent. or about $\%$

Question

When two six-sided dice are rolled, there are 363636​ possible outcomes.a. Find the probability that the sum is not 444​ . Express your first answer as a fraction in simplest form, and round your percent answer to the nearest whole percent. or about %\%%​b. Find the probability that the sum is greater than 555​ . Express your first answer as a fraction in simplest form, and round your percent answer to the nearest whole percent. or about %\%

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Solution

a. The sum of 4 can be achieved by the following combinations: (1,3), (2,2), (3,1). That's 3 out of 36 possible outcomes. Therefore, the probability that the sum is not 4 is 1 - (3/36) = 33/36. In percentage, this is approximately 92%.

b. The sums greater than 5 can be achieved by the following combinations: (2,4), (2,5), (2,6), (3,3), (3,4), (3,5), (3,6), (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). That's 24 out of 36 possible outcomes. Therefore, the probability that the sum is greater than 5 is 24/36 = 2/3. In percentage, this is approximately 67%.

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