Suppose a special 40-sided die is rolled once where each face is marked with a number 1 through 40. What is the probability that the die lands on a 13 or a 10?

To solve the problem, we need to find the probability that the die lands on either a 13 or a 10 when rolled once.

### Step 1: Identify the total number of possible outcomes
Since the die is a 40-sided die, each face is numbered from 1 to 40. Therefore, the total number of possible outcomes is:
\[
\text{Total outcomes} = 40
\]

### Step 2: Identify the favorable outcomes
The favorable outcomes are the die landing on a 13 or a 10. These are two specific outcomes, so the number of favorable outcomes is:
\[
\text{Favorable outcomes} = 2
\]

### Step 3: Calculate the probability
The probability of an event is calculated as the ratio of the number of favorable outcomes to the total number of possible outcomes:
\[
\text{Probability} = \frac{\text{Favorable outcomes}}{\text{Total outcomes}} = \frac{2}{40} = \frac{1}{20}
\]

Thus, the probability that the die lands on a 13 or a 10 is:
\[
\boxed{\frac{1}{20}}
\]

Would you like more details on any of the steps, or do you have further questions?

Here are five related questions to deepen your understanding:
1. What is the probability that the die lands on a number other than 13 or 10?
2. If the die is rolled twice, what is the probability of landing on 13 in the first roll and 10 in the second?
3. How does the probability change if the die has 50 sides instead of 40?
4. What is the probability of landing on any prime number between 1 and 40?
5. What is the probability of rolling an even number on this 40-sided die?

**Tip:** In probability, events are mutually exclusive if they cannot happen at the same time (like rolling a 13 and a 10 on a single roll). This is why you can simply add probabilities when looking for "or" events in such cases!

Find out how to calculate the probability of rolling a 13 or a 10 on a 40-sided die. This problem covers basic probability concepts and is suitable for students in Grades 6-8. Includes step-by-step calculations.

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