You roll a 44-sided die and note the number on the bottom, 1,2,3,41,2,3,4. (A 44-sided die is shaped like a pyramid, so when it comes to rest, there’s no single side facing up.) Identify the sample space when rolling this die one time.

Provide your answer below:

When rolling a 4-sided die (often called a tetrahedral die), the sample space is the set of all possible outcomes that can occur. Since the die has four sides labeled \(1, 2, 3,\) and \(4\), the sample space includes all of these numbers.

The sample space \( S \) when rolling this die one time is:

\[
S = \{1, 2, 3, 4\}
\]

This set represents all possible outcomes of a single roll of the die.

Would you like further details or have any other questions?

Here are some related questions:
1. What is the probability of rolling a 1 on a 4-sided die?
2. How would the sample space change if the die had 6 sides?
3. What is the probability of rolling an even number on a 4-sided die?
4. If you roll the die twice, what is the sample space for the two rolls?
5. How would you calculate the expected value of a roll of this 4-sided die?

**Tip:** When determining a sample space, list all possible distinct outcomes for the event you're considering.

Understand the concept of sample space by identifying all possible outcomes when rolling a 4-sided die. This problem explores basic probability theory and is suitable for students in Grades 5-6.

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