Question

Use the theoretical probability formula to solve the following problem. Express the probability as a fraction reduced to lowest terms.
A​ 12-sided die is rolled. The set of equally likely outcomes is StartSet 1 comma 2 comma 3 comma 4 comma 5 comma 6 comma 7 comma 8 comma 9 comma 10 comma 11 comma 12 EndSet . Find the probability of rolling a number greater than 12.
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Part 1
The probability of rolling a number greater than 12 is
  
enter your response here.
​(Type an integer or a simplified​ fraction.)

Answer 1

To find the probability of rolling a number greater than 12 on a 12-sided die, we can use the theoretical probability formula, which is given by:

\[
P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}
\]

In this case:

- **Total number of possible outcomes**: Since the die has 12 sides, there are 12 possible outcomes (1 through 12).
- **Number of favorable outcomes**: There are no outcomes that are greater than 12 on a 12-sided die. Thus, the number of favorable outcomes is 0.

Now we can substitute these values into the probability formula:

\[
P(\text{greater than 12}) = \frac{0}{12}
\]

This simplifies to:

\[
P(\text{greater than 12}) = 0
\]

So, the probability of rolling a number greater than 12 is

\[
\text{0}
\]