# Ch 18: Understanding Probability, Combinations & Permutations

### About This Chapter

## Understanding Probability, Combinations & Permutations - Chapter Summary

Study the basics of probability, combinations and permutations at home or anywhere you can access the Internet. This chapter's entertaining online lessons examine expected value in probability, the fundamental counting principle, math combinations and more. By the end of this chapter, you will be able to:

- Calculate simple conditional probabilities
- Discuss the probability of dependent and independent events
- Define expected value in probability
- Use the fundamental counting principle
- Utilize the formula for math combinations
- Calculate a permutation and the probability of combinations and permutations

Review the lessons in any manner that helps you best understand probability, combinations and permutations. All the lessons in this chapter are available as videos or written transcripts and can be accessed any time via any computer, smartphone or tablet. Short quizzes accompanying the lessons let you test your comprehension of their contents. A practice exam is also available to check your knowledge of this entire chapter.

### 1. How to Calculate Simple Conditional Probabilities

Conditional probability, just like it sounds, is a probability that happens on the condition of a previous event occurring. To calculate conditional probabilities, we must first consider the effects of the previous event on the current event.

### 2. Probability of Independent and Dependent Events

Sometimes probabilities need to be calculated when more than one event occurs. These types of compound events are called independent and dependent events. Through this lesson, we will look at some real-world examples of how to calculate these probabilities.

### 3. Expected Value in Probability: Definition & Formula

After watching this video lesson, you will understand what expected value means. You will learn how to use this value to decide whether a certain action is worth taking or not.

### 4. How to Use the Fundamental Counting Principle

There are many situations in which you will have to make several decisions simultaneously. The fundamental counting principle will help you determine how many different possible outcomes there are when you have to make multiple simultaneous decisions.

### 5. Math Combinations: Formula and Example Problems

Combinations are an arrangement of objects where order does not matter. In this lesson, the coach of the Wildcats basketball team uses combinations to help his team prepare for the upcoming season.

### 6. How to Calculate the Probability of Combinations

To calculate the probability of a combination, you will need to consider the number of favorable outcomes over the number of total outcomes. Combinations are used to calculate events where order does not matter. In this lesson, we will explore the connection between these two essential topics.

### 7. How to Calculate a Permutation

A permutation is a method used to calculate the total outcomes of a situation where order is important. In this lesson, John will use permutations to help him organize the cards in his poker hand and order a pizza.

### 8. How to Calculate the Probability of Permutations

In this lesson, you will learn how to calculate the probability of a permutation by analyzing a real-world example in which the order of the events does matter. We'll also review what a factorial is. We will then go over some examples for practice.

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### Other Chapters

Other chapters within the ISEE Upper Level: Practice & Study Guide course

- Verbal Reasoning Skills Development
- Types of Reading Strategies
- Understanding Narrative Texts
- Interpreting & Analyzing Reading Passages
- Brainstorming & Organization in Writing
- Understanding Syntax & Sentence Structure
- Understanding Essay Writing
- Writing & Revising Strategies
- Quantitative Reasoning in Math
- Types of Numbers, Number Lines & Operations
- Overview of Whole Numbers & Integers
- Irrational, Rational & Complex Numbers
- How to Use Estimation in Math
- Decimal Conversion & Problem-Solving
- Solving Operations with Fractions
- Understanding Exponents & Exponential Expressions
- Overview of Matrices & Vectors
- How to Solve & Graph Inequalities
- Overview of the Properties of Functions
- Understanding Graphs of Functions
- Understanding Sequences & Series in Math
- Fundamental Concepts in Geometry
- Coordinate Geometry & Transformations
- Understanding Triangles & Triangle Congruence
- Measuring Shapes in Geometry
- Visual Displays of Data
- Statistics & Data Analysis
- ISEE Upper Level Flashcards