Introduction:
When two dice are thrown at the same time, the product of the numbers appearing on their faces is noted. In this problem, we need to find the probability that the product is between 8 and 13.

Understanding the problem:
To solve this problem, we need to determine the total number of possible outcomes and the number of favorable outcomes. The probability is then calculated by dividing the number of favorable outcomes by the total number of outcomes.

Calculating the total number of outcomes:
When two dice are thrown, each dice has 6 possible outcomes (numbers 1 to 6). As the two dice are thrown simultaneously, the total number of outcomes can be calculated by multiplying the number of outcomes for each dice.

Total number of outcomes = 6 × 6 = 36

Calculating the number of favorable outcomes:
To find the favorable outcomes, we need to determine the possible combinations of numbers whose product is between 8 and 13. We can list down all the possible combinations and count them.

Possible combinations with a product between 8 and 13:
- 2 × 4 = 8
- 3 × 3 = 9
- 4 × 2 = 8
- 6 × 2 = 12

Therefore, there are 4 favorable outcomes.

Calculating the probability:
The probability is calculated by dividing the number of favorable outcomes by the total number of outcomes.

Probability = Number of favorable outcomes / Total number of outcomes
Probability = 4 / 36
Probability = 1 / 9

Conclusion:
The probability that the product of the two dice is between 8 and 13 is 1/9.

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