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Sample Space

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Sample Space

Study Guide

Key Definition

A sample space is the set of all possible outcomes of an experiment, such as ${H, T}$ for a coin flip or ${1, 2, 3, 4, 5, 6}$ for a die roll.

Important Notes

Sample spaces can vary in size depending on the experiment.
The notation ${}$ is used to represent a set.
Sample spaces are fundamental in probability calculations.
Each outcome in a sample space is equally likely if the experiment is fair.
Understanding sample spaces helps in predicting results of experiments.

Mathematical Notation

${}$ denotes a set of outcomes

$∪$ represents the union of sets

$∩$ represents the intersection of sets

$|S|$ represents the number of elements in set $S$

Remember to use proper notation when solving problems

Why It Works

Understanding sample space allows us to calculate probabilities by considering all possible outcomes and determining the likelihood of each.

Remember

The sample space provides a complete list of possible outcomes, which is crucial for calculating probabilities.

Quick Reference

Coin Flip:${H, T}$

Die Roll:${1, 2, 3, 4, 5, 6}$

Understanding Sample Space

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

A sample space is the list of all possible outcomes of an experiment, like ${H, T}$ for a coin flip.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is the sample space for rolling a six-sided die?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

A teenager has a bag with 3 red, 2 blue, and 5 green marbles. What is the sample space when drawing one marble?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Consider a deck of cards. What is the sample space when drawing one card?

Challenge Quiz

Single Choice Quiz

Advanced

What is the sample space for flipping two coins?

Recap

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Review key concepts and takeaways