To calculate the probability of Event A, which is rolling a number less than 8 on a 12-sided die, we follow these steps:

1. Total Possible Outcomes

A 12-sided die has 12 faces, so the total number of possible outcomes is 12.

2. Favorable Outcomes

The numbers less than 8 on the die are: $1, 2, 3, 4, 5, 6, 7$ There are 7 favorable outcomes (numbers less than 8).

3. Probability Formula

The probability of an event is given by the formula: $P(\text{Event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$ So, for this problem: $P(A) = \frac{7}{12}$

Conclusion

The probability of rolling a number less than 8 is $\frac{7}{12}$.

Would you like more details or examples? Here are a few related questions to explore:

1. What is the probability of rolling a number greater than 8?
2. What is the probability of rolling an even number on this 12-sided die?
3. If the die is rolled twice, what is the probability that both rolls result in numbers less than 8?
4. How would the probability change if the die had 20 sides instead of 12?
5. What is the probability of rolling a prime number on this 12-sided die?

Tip: To simplify probability problems, always begin by identifying the total possible outcomes and the favorable ones.