Question 22 **pts**

You conduct the following experiment: You throw a fair six-sided die three times in a row and you note down the top number after every throw. Every throw is independent of the others. You combine the three numbers together to one element "(1st result, 2nd result, 3rd result)".

How many elements are in the sample space?

To determine the number of elements in the sample space for this experiment, we need to consider the following:

1. **Each die throw is independent**: This means that the outcome of one throw does not affect the others.
2. **Six possible outcomes per throw**: Since the die is fair and six-sided, each throw can result in one of six numbers: 1, 2, 3, 4, 5, or 6.
3. **Three throws in total**: The experiment involves throwing the die three times.

For each of the three throws, there are 6 possible outcomes. Since the outcomes are independent, the total number of possible outcomes (i.e., the number of elements in the sample space) is the product of the number of possible outcomes for each throw:

\[
\text{Total number of elements in the sample space} = 6 \times 6 \times 6 = 6^3
\]

\[
6^3 = 216
\]

So, the sample space consists of **216** elements.

Would you like further details or have any questions? 

Here are 5 related questions you might find interesting:
1. What would the sample space be if the die was thrown four times instead of three?
2. How does the sample space change if the die is biased?
3. What is the probability of getting the sequence (2, 4, 6) in this experiment?
4. How many outcomes would there be if the die had 8 sides instead of 6?
5. How would the sample space change if you recorded the sum of the numbers instead of the sequence?

**Tip:** Understanding the concept of independent events is crucial in probability, as it simplifies the calculation of combined outcomes.

Understand how to calculate the sample space when rolling a fair six-sided die three times independently. Learn the multiplication principle for independent events in probability. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation