# Ch 15: Probability Concepts in Math

### About This Chapter

## Probability Concepts in Math - Chapter Summary

In these lessons, you'll receive a refresher on probability concepts in math, including topics like calculating conditional probabilities, determining the probability of overlapping events, using math combinations, and calculating binomial distribution. You'll also take a look at calculating the probability for independent and dependent events. After completing the chapter, you should be able to do the following:

- Use the formula for classical probability
- Convert probabilities to percentages
- Explain how randomized experiments are designed
- Obtain information using simple random sampling
- Describe the properties of different types of random variables
- Explore the idea of events as subsets
- Provide real world examples of different forms of probability and how to calculate them
- Explain the 'at least one' rule, the central limit theorem, and Bayes' theorem

Our subject matter experts use these short video lessons to help you better understand probability concepts in math. There are plenty of examples provided to ensure you grasp the various concepts covered. The video timelines let you easily navigate the videos and focus the topics that you need to review most. A brief multiple-choice quiz is available for each lesson to test your knowledge.

### 1. Classical Probability: Definition, Approach & Examples

In this lesson, you will learn about classical probability, its formula, and how to convert probability to percentages. You will have a chance to practice your newfound skills with several examples.

### 2. 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.

### 3. How Randomized Experiments Are Designed

When reading research or when conducting your own, it is important to understand the basic concepts of randomized experimental design that are covered in this lesson.

### 4. Simple Random Samples: Definition & Examples

Simple random sampling is a common method used to collect data in many different fields. From psychology to economics, simple random sampling can be the most feasible way to get information. Learn all about it in this lesson!

### 5. Random Variables: Definition, Types & Examples

This lesson defines the term random variables in the context of probability. You'll learn about certain properties of random variables and the different types of random variables.

### 6. 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.

### 7. 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.

### 8. 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.

### 9. 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.

### 10. 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.

### 11. Finding Probabilities About Means Using the Central Limit Theorem

The central limit theorem provides us with a very powerful approach for solving problems involving large amount of data. In this lesson, we'll explore how this is done as well as conditions that make this theorem valid.

### 12. Bayes' Theorem Practice Problems

Bayes' theorem is a formula used for computing conditional probability, which is the probability of something occurring with the prior knowledge that something else has occurred. In this lesson, you'll learn how to use Bayes' theorem while completing some practice problems.

### 13. 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.

### 14. Binomial Distribution: Definition, Formula & Examples

You have a probability distribution to create, which one do you use? That depends. In this lesson, learn about binomial distributions, get examples and criteria for their use, and learn how to calculate the binomial distribution formula.

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### Other Chapters

Other chapters within the NDA Exam Preparation & Study Guide course

- About the NDA Exam
- Algebra Concepts
- Advanced Algebra Concepts
- Solving Matrices & Determinants
- Trigonometry Concepts
- Geometry & Linear Equations
- Analytic Geometry
- Functions, Limits & Continuity
- Derivative Rules
- Calculations & Applications of Derivatives
- Integral Calculus
- Differential Equations & Applications
- Scalars & Vectors in Algebra
- Visualizing Statistics
- Grammar and Usage
- Improving Reading Comprehension
- Measurements in Physics
- Motion in Physics
- Basics of Work, Power & Energy
- Understanding Heat Transfer
- Sound Waves
- Light, Mirrors & Lenses
- Magnets
- Electric Currents & Power
- Scientific Technology, Machines & Tools
- The Atom & Structure of Elements
- Chemical Properties of Elements & Substances
- Chemical Symbols, Formulas & Reactions
- Qualities of Living Organisms
- Health Science Basics
- Solar System & Eclipses
- Achievements of Famous Scientists
- Indian History
- Overview of Major World History Events
- World Government Types
- The Earth
- Earth's Oceans, Atmosphere & Climate
- Regional Geography of South Asia
- Modern Day Events in India
- NDA Exam Preparation & Study Guide Flashcards