What is the probability of getting sum as 9 or higher when two dice are thrown?
Last Updated :
13 Feb, 2024
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: There are 4 combinations of outcomes that result in a sum of 9: (3, 6), (4, 5), (5, 4), and (6, 3).
- For a sum of 10: There are 3 combinations of outcomes that result in a sum of 10: (4, 6), (5, 5), and (6, 4).
- For a sum of 11: There are 2 combinations of outcomes that 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:
- Approximation:
- The probability simplifies to , 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.
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