What is the probability of getting sum as 9 or higher when two dice are thrown? Last Updated : 23 Jul, 2025 Comments Improve Suggest changes Like Article Like Report Answer: The probability of getting a sum of 9 or higher when two dice are thrown is approximately 0.2778.Let's break down the explanation:When two dice are thrown, each die can land on any number from 1 to 6, inclusive. To calculate the probability of getting a sum of 9 or higher, we need to count the number of outcomes where the sum of the numbers on the faces of the two dice is 9, 10, 11, or 12.1. Counting Favorable Outcomes:For a sum of 9: 4 combinations of outcomes result in a sum of 9: (3, 6), (4, 5), (5, 4), and (6, 3).For a sum of 10: 3 combinations of outcomes result in a sum of 10: (4, 6), (5, 5), and (6, 4).For a sum of 11: 2 combinations of outcomes result in a sum of 11: (5, 6) and (6, 5).For a sum of 12: There is 1 combination of outcomes that result in a sum of 12: (6, 6).So, in total, there are 4+3+2+1=10 favorable outcomes.2. Total Number of Possible Outcomes:When two dice are thrown, there are a total of 6×6=36 possible outcomes.3. Calculating Probability:The probability of getting a sum of 9 or higher is the ratio of the number of favorable outcomes to the total number of possible outcomes:\text{Probability} = \frac{36}{10} Approximation:The probability \frac{10}{36} simplifies to \frac{5}{18} , which is approximately 0.2778 when expressed as a decimal.Interpretation:This means that approximately 27.78% of the time when two dice are thrown, the sum of the numbers on the faces of the two dice will be 9 or higher.In summary, the probability of getting a sum of 9 or higher when two dice are thrown is approximately 0.2778.1. What is the probability of getting a sum of exactly 8 when two dice are thrown?Outcomes for a sum of 8: (2,6), (3,5), (4,4), (5,3), (6,2) — 5 outcomesTotal possible outcomes: 36Probability: 5/362. What is the probability of getting a sum of 7 or 11 when two dice are thrown?Outcomes for a sum of 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) — 6 outcomesOutcomes for a sum of 11: (5,6), (6,5) — 2 outcomesTotal favorable outcomes: 6 (sum of 7) + 2 (sum of 11) = 8Probability: 8/36 = 2/93. What is the probability of getting a sum less than 4 when two dice are thrown?Outcomes for a sum of 2: (1,1) — 1 outcomeOutcomes for a sum of 3: (1,2), (2,1) — 2 outcomesTotal favorable outcomes: 1 + 2 = 3Probability: 3/36 = 1/124. What is the probability of getting a sum of 6 or 8 when two dice are thrown?Outcomes for a sum of 6: (1,5), (2,4), (3,3), (4,2), (5,1) — 5 outcomesOutcomes for a sum of 8: (2,6), (3,5), (4,4), (5,3), (6,2) — 5 outcomesTotal favorable outcomes: 5 (sum of 6) + 5 (sum of 8) = 10Probability: 10/36 = 5/18Related Articles:What is the most likely score from throwing two dice?What is the probability of getting a sum less than 9, when two dice are thrown simultaneously? 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