To find the probability of Event A (rolling a number greater than 4) when rolling a 12-sided die, follow these steps:

Step 1: Identify the total number of possible outcomes

Since the die is 12-sided and numbered from 1 to 12, the total number of possible outcomes is 12.

Step 2: Identify the favorable outcomes

Event A is defined as rolling a number greater than 4. So, the favorable outcomes are any number from 5 to 12. These outcomes are: $5, 6, 7, 8, 9, 10, 11, 12$

There are 8 favorable outcomes (5, 6, 7, 8, 9, 10, 11, 12).

Step 3: Calculate the probability

The probability $P(A)$ of Event A is the ratio of favorable outcomes to the total number of possible outcomes: $P(A) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{8}{12}$

Step 4: Simplify the fraction

Simplify the fraction: $P(A) = \frac{8}{12} = \frac{2}{3}$

Final Answer:

The probability of rolling a number greater than 4 is $\frac{2}{3}$.

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Would you like a more detailed explanation or have any questions? Here are a few related questions you might be interested in:

1. What is the probability of rolling a number less than or equal to 4 on the same die?
2. What is the probability of rolling an even number on the 12-sided die?
3. How does the probability change if the die were 6-sided instead of 12-sided?
4. What are the odds in favor of rolling a number greater than 4 on this die?
5. What is the probability of rolling a number that is either prime or greater than 4?

Tip: Always simplify probabilities to their lowest terms for the clearest answer!