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.
- The probability
- 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 outcomes
Total possible outcomes: 36
Probability: 5/36
2. 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 outcomes
Outcomes for a sum of 11: (5,6), (6,5) — 2 outcomes
Total favorable outcomes: 6 (sum of 7) + 2 (sum of 11) = 8
Probability: 8/36 = 2/9
3. 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 outcome
Outcomes for a sum of 3: (1,2), (2,1) — 2 outcomes
Total favorable outcomes: 1 + 2 = 3
Probability: 3/36 = 1/12
4. 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 outcomes
Outcomes for a sum of 8: (2,6), (3,5), (4,4), (5,3), (6,2) — 5 outcomes
Total favorable outcomes: 5 (sum of 6) + 5 (sum of 8) = 10
Probability: 10/36 = 5/18
