# Ch 33: NYSTCE Mathematics: Probability

### About This Chapter

## NYSTCE Mathematics: Probability - Chapter Summary

These lessons aim to help you prepare for the questions regarding probability on the NYSTCE Mathematics exam. You will be given the opportunity to review mathematical sets and how to calculate simple conditional probabilities. Additionally, this chapter goes over the calculation of probability in applicable mathematical areas, providing an efficient and effective review of the following:

- Events as subsets of a sample space
- Using venn diagrams to show conjunctions and disjunctions
- The probability of independent and dependent events
- The relationship between conditional probabilities and independence
- Applying conditional probability and independence to real-life situations
- The addition and multiplication rules of probability
- Probability of simple, compound, and complementary events

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### 1. Mathematical Sets: Elements, Intersections & Unions

Today we're going to explore mathematical sets, which are surprisingly simple! Sets are just collections of any objects or concepts, also known as elements, that can be related to each other through union or intersection.

### 2. Events as Subsets of a Sample Space: Definition & Example

Probability can get very confusing at times. You will find that some words, such as events and subsets, are often referring to the same concept depending on the experiment. Use this lesson to understand the concept of events as subsets.

### 3. Using Venn Diagrams to Show Conjunctions & Disjunctions

Watch this video lesson to learn how you can use a Venn diagram to show conjunctions and disjunctions. You will see what a conjunction looks like and what a disjunction looks like in a Venn diagram.

### 4. 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.

### 5. 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.

### 6. 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.

### 7. The Relationship Between Conditional Probabilities & Independence

Conditional and independent probabilities are a basic part of learning statistics. It's important that you can understand the similarities and differences between the two as discussed in this lesson.

### 8. Applying Conditional Probability & Independence to Real Life Situations

It can be really confusing learning how to apply conditional and independent probability to real-life situations. This lesson focuses on several examples and practice problems to help you learn how to find conditional probability.

### 9. The Addition Rule of Probability: Definition & Examples

In this lesson, you will learn the differences between mutually exclusive and non-mutually exclusive events and how to find the probabilities of each using the Addition Rule of Probability.

### 10. The Multiplication Rule of Probability: Definition & Examples

The Multiplication Rule of Probability is a concept you will use frequently when solving probability equations. In this lesson, learn the two different scenarios in which you will use the multiplication rule of probability.

### 11. 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.

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### Other Chapters

Other chapters within the NYSTCE Mathematics (004): Practice & Study Guide course

- NYSTCE Mathematics: Fractions, Decimals & Percents
- NYSTCE Mathematics: Complex Numbers
- NYSTCE Mathematics: Factoring & Divisibility
- NYSTCE Mathematics: Exponents
- NYSTCE Mathematics: Patterns & Functions
- NYSTCE Mathematics: Understanding Algebraic Expressions
- NYSTCE Mathematics: Solving Algebraic Equations
- NYSTCE Mathematics: Linear Equations
- NYSTCE Mathematics: Quadratic Functions
- NYSTCE Mathematics: Polynomial Functions
- NYSTCE Mathematics: Exponential Expressions
- NYSTCE Mathematics: Absolute Value Expressions
- NYSTCE Mathematics: Rational Expressions
- NYSTCE Mathematics: Radical Expressions
- NYSTCE Mathematics: Exponential & Logarithmic Functions
- NYSTCE Mathematics: Trigonometry
- NYSTCE Mathematics: Applications of Trigonometry
- NYSTCE Mathematics: Calculus Concepts
- NYSTCE Mathematics: Calculus Applications
- NYSTCE Mathematics: Principles of Measurement
- NYSTCE Mathematics: Lines & Angles
- NYSTCE Mathematics: Parallel Lines & Symmetry
- NYSTCE Mathematics: Geometric Construction
- NYSTCE Mathematics: Geometric Shapes
- NYSTCE Mathematics: Triangle Proofs & Theorems
- NYSTCE Mathematics: Geometric Solids
- NYSTCE Mathematics: Conic Sections
- NYSTCE Mathematics: Vector Operations
- NYSTCE Mathematics: Transformations in Geometry
- NYSTCE Mathematics: Coordinate Geometry
- NYSTCE Mathematics: Sequences & Series
- NYSTCE Mathematics: Counting Strategies
- NYSTCE Mathematics: Probability Distributions
- NYSTCE Mathematics: Data Analysis & Statistics
- NYSTCE Mathematics: Sampling & Prediction
- NYSTCE Mathematics: Regression & Correlation
- NYSTCE Mathematics: Discrete Mathematics
- NYSTCE Mathematics Flashcards