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: 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.