What is the probability of getting sum as 9 or higher when two dice are thrown?

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:

• 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.

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

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• What is the probability of getting a sum less than 9, when two dice are thrown simultaneously?