# Ch 22: Probability Calculations

### About This Chapter

## Probability Calculations - Chapter Summary and Learning Objectives

Mathematicians can determine the likelihood of an event happening by using probability calculations. These calculations take statistical data to determine how often something might occur and what factors may affect the likelihood of that event occurring. The lessons provided in this chapter give you an easy-to-follow guide that walks you through these probability calculations. You will also learn the definitions of all related terms. Therefore, this chapter can give you a deeper understanding of the following:

- Probability calculations with permutations and combinations
- The effects of dependent and independent events on probability calculations
- Understanding how different types of events change probability formulas
- Applying the 'At Least One' Rule and the Either/Or scenario to calculations

Lesson | Objective |
---|---|

How to Calculate the Probability of Permutations | Study factorials, go through the steps for determining the probability of a permutation, and examine a permutation example where events must happen in a certain order. |

How to Calculate the Probability of Combinations | Measure the amount of favorable outcomes and divide that by the amount of total outcomes, figure out the amount of events if no order is required, and show the relationship between these two concepts. |

Probability of Independent and Dependent Events | Practice calculating the probability of compound events by identifying dependent and independent events. |

Probability Distribution: Definition, Formula & Example | Go through the steps for building a probability distribution map that highlights all possible results pertaining to a statistical event. |

Probability of Simple, Compound and Complementary Events | Establish the formulas for calculating these three different types of events, then apply the formulas to practical examples. |

Either/Or Probability: Overlapping and Non-Overlapping Events | Evaluate statistical data, then determine the probability of either/or events with both non-overlapping and overlapping events. |

Probability of Independent Events: The 'At Least One' Rule | Delve into the definition for the process of complementary events, learn the 'At Least One' Rule, and use this information to determine independent event probabilities. |

How to Calculate Simple Conditional Probabilities | Point out the factors that create conditional probability, determine how the sequence of previous events to current events affects probability calculations, and practice calculating conditional probabilities. |

### 1. 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.

### 2. 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.

### 3. 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.

### 4. Probability Distribution: Definition, Formula & Example

Probability distribution is a way of mapping out the likelihood of all the possible results of a statistical event. In this lesson, we'll look at how that is done and how to make practical applications of this concept.

### 5. Probability of Simple, Compound and Complementary Events

Simple, compound, and complementary events are different types of probabilities. Each of these probabilities are calculated in a slightly different fashion. In this lesson, we will look at some real world examples of these different forms of probability.

### 6. Either/Or Probability: Overlapping and Non-Overlapping Events

Statistics is the study and interpretation of a set of data. One area of statistics is the study of probability. This lesson will describe how to determine the either/or probability of overlapping and non-overlapping events.

### 7. Probability of Independent Events: The 'At Least One' Rule

Occasionally when calculating independent events, it is only important that the event happens once. This is referred to as the 'At Least One' Rule. To calculate this type of problem, we will use the process of complementary events to find the probability of our event occurring at least once.

### 8. 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.

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### Other Chapters

Other chapters within the Intermediate Algebra for College Students course

- Algebra Review
- Number Theory Principles
- Exponents & Their Properties
- Radicals
- Polynomials
- Rational Expressions & Practice
- Linear Equations, Systems & Graphs
- Linear Inequalities
- Absolute Value Expressions & Graphs
- Complex Numbers, Forms & Graphs
- Quadratic Equations & Solutions
- Logarithmic & Trigonometric Equations
- Cartesian Coordinate System
- Linear Models
- Types of Functions
- Graphing & Transforming Functions
- Quadratic & Polynomial Functions
- Operations on Functions
- Real, Complex & Rational Zeros
- Rational Functions & Inequalities
- Pythagorean Theorem
- Measurement & Unit Conversion