Back To Course

Math 102: College Mathematics14 chapters | 108 lessons

Watch short & fun videos
**Start Your Free Trial Today**

Start Your Free Trial To Continue Watching

As a member, you'll also get unlimited access to over

Your next lesson will play in
10 seconds

Lesson Transcript

Instructor:
*Jennifer Beddoe*

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.

'What are the chances?' It's probably a question you hear or say quite often, and it can be used in many different situations:

'What are the chances of winning the lottery tonight?'

'What are the chances of our team winning today?'

'What are the chances you'll get an A on the next test?'

Determining the chances of an event occurring is called **probability**. Probability is most often written as a percent, but it can also be written as a fraction. The higher the percent, or the closer the fraction is to one, the greater the likelihood that an event will occur. If you have a 90% chance of passing your test, it is quite likely you will pass. On the other hand, if you have a 1/1,000,000 chance of winning the lottery, you are better off saving the cost of the ticket.

**Either/or probability** refers to the probability that one event or the other will occur. For example, what is the probability that you will draw a Jack or a three from a normal deck of cards? Or, what is the probability that you will roll a 3 or a 5 when rolling a normal 6-sided die? To solve this type of probability problem, here is the formula you will use:

*P*(*A* or *B*) = *P*(*A*) + *P*(*B*)

To find the probability of each event, simply divide the amount of **favorable events** by the amount of **total events**. A favorable event is an event that you want to occur. In the earlier card question, the favorable event is drawing either a Jack or a three. The total number of events is the total number of things that could occur, whether favorable or not.

So, to continue on and solve this card drawing question, we have determined that *A* is the probability of drawing a Jack, and *B* is the probability of drawing a three.

There are 4 Jacks in a normal deck of cards, so the number of favorable events (drawing a Jack) is 4. The total number of events is 52 since there are 52 cards in a deck of cards. This means that the probability of drawing a Jack is 4/52, which can be reduced to 1/13.

*P*(*B*), or the probability of drawing a three, is also 1/13 because there are 4 threes in a deck of cards and, as before, there are 52 total cards in the deck.

To finish answering the question and find the probability of drawing either a Jack or a three, we use the equation *P*(*A* or *B*) = *P*(*A*) + *P*(*B*). *P*(*A* or *B*) is equal to 1/13 + 1/13, which is 2/13

To solve the dice question mentioned earlier, follow the same steps. *P*(*A*), or the probability of rolling a 3, is 1/6. There is one 3 (the favorable event) and 6 sides on the die (the total events).

*P*(*B*) is the probability of rolling a 5 and it's the same, 1/6. Therefore, the probability of rolling either a 3 or a 5 is *P*(*A* or *B*) is equal to 1/6 + 1/6, which is 2/6, or 1/3.

These events are called **non-overlapping events**, or events that are independent of each other. There are also **overlapping events**, which are events that are not independent of each other.

An example of an overlapping event would be, 'What is the probability of drawing a seven or a diamond from a standard deck of cards?' Since there is a seven of diamonds, there is one card in the deck that is both a seven and a diamond. This has to be accounted for in the equation. If you don't, you will end up with the incorrect probability. The equation for determining the either/or probability of overlapping events is:

*P*(*A* or *B*) = *P*(*A*) + *P*(*B*) - *P*(*A* and *B*).

As you can see, you must subtract out the probability of the overlapping event to get the right answer. The first event (drawing a seven), has a probability of 4/52 because there are 4 sevens in the deck. The second favorable event (drawing a diamond) is 13/52. The overlap event (drawing the seven of diamonds) has a probability of 1/52.

Now, if we put all those numbers in the probability equation, we can determine that the probability of drawing either a seven or a diamond from a regular deck of cards is 4/52 + 13/52 - 1/52, which is 16/52, or 4/13. The probability of pulling a seven or a diamond from a normal deck of cards is 4/13.

Let's try one more example:

The numbers 1 through 20 are written on separate slips of paper and placed in a hat. One of the slips is randomly drawn. What is the probability that either an even or a prime number is drawn?

In the numbers from 1 to 20, there are 10 even numbers (2, 4, 6, 8, 10, 12, 14, 16, 18 and 20). Therefore, *P*(*A*) is 10/20. There are 8 prime numbers (2, 3, 5, 7, 11, 13, 17 and 19), so *P*(*B*) is 8/20.

The overlap between the two groups includes only the number 2. So, *P*(*A* + *B*) is 1/20. The equation is 10/20 + 8/20 - 1/20, which is equal to 17/20.

**Probability** is the chance that something is or is not going to happen. To determine the probability of an event, you need to determine the number of **favorable events** and divide that by the number of **total events** that could happen. To determine the probability of one event or another occurring, you first need to determine if the events are **overlapping** or **non-overlapping**. If they do not overlap, then you just need to add the probability of each event occurring together. If there is some overlap, then to get the true probability, you must also subtract out the probability of the overlapping event.

Once you've viewed this video lesson, you might have the knowledge required to:

- Know what it takes to determine an event's probability
- Differentiate between overlapping and non-overlapping events
- Find the probability of both overlapping and non-overlapping events

To unlock this lesson you must be a Study.com Member.

Create your account

Already a member? Log In

BackDid you know… We have over 79 college courses that prepare you to earn credit by exam that is accepted by over 2,000 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

You are viewing lesson
Lesson
7 in chapter 13 of the course:

Back To Course

Math 102: College Mathematics14 chapters | 108 lessons

- Go to Logic

- Go to Sets

- Understanding Bar Graphs and Pie Charts 9:36
- How to Calculate Percent Increase with Relative & Cumulative Frequency Tables 5:47
- How to Calculate Mean, Median, Mode & Range 8:30
- Calculating the Standard Deviation 13:05
- Probability of Simple, Compound and Complementary Events 6:55
- Probability of Independent and Dependent Events 12:06
- Either/Or Probability: Overlapping and Non-Overlapping Events 7:05
- How to Calculate Simple Conditional Probabilities 5:10
- Math Combinations: Formula and Example Problems 7:14
- How to Calculate the Probability of Combinations 11:00
- How to Calculate a Permutation 6:58
- How to Calculate the Probability of Permutations 10:06
- Go to Probability and Statistics

- DSST Principles of Advanced English Composition: Study Guide & Test Prep
- Upper Level SSAT: Test Prep & Practice
- The Adventures of Sherlock Holmes Study Guide
- Sherlock Holmes Short Stories Study Guide
- PTE Academic Test: Practice & Study Guide
- Finding, Evaluating & Using Sources
- Revising & Editing an Essay
- Citing & Documenting Sources
- Analyzing Arguments in Writing
- Audience & Goal In Writing
- TOEIC Listening & Reading Test: Purpose & Format
- Excelsior College BS in Business Degree Plan Using Study.com
- IELTS General Training Reading: Format & Task Types
- IELTS General Training Writing: Format & Task Types
- Gates-MacGinitie Reading Test Scores
- IELTS General Training Test: Structure & Scoring
- Supply and Demand Activities for Kids

- Updating the Project Schedule & Dealing with Change
- Hotel Housekeeping: Standards & Checklist
- Capital Requirements: Definition & Explanation
- Holistic Perspective in Anthropology: Definition & Approach
- Special Education Transition Plans from Middle School to High School
- Spartan Traditions: Festivals & History
- American Colonial Music: Instruments & Facts
- Strategies for Teaching Manners to Students with Autism
- Quiz & Worksheet - Personal Finance & Consumer Skills
- Quiz & Worksheet - Financial Markets
- Quiz & Worksheet - History of the Hospitality Industry
- Quiz & Worksheet - Cultural Norms in Central America
- Quiz & Worksheet - The Soldier by Rupert Brooke
- Muscle Contraction Flashcards
- Water Polo Flashcards

- History of the Vietnam War: Certificate Program
- Western Civilization 1648 to the Present: Help and Review
- AP Music Theory Syllabus Resource & Lesson Plans
- SAT Mathematics Level 2: Help and Review
- ACT English Section: Prep & Practice
- The Elizabethan Era: Tutoring Solution
- The 1970s (1969-1979): Help and Review
- Quiz & Worksheet - Characteristics & Types of Plankton
- Quiz & Worksheet - The Five Motives of Imperialism
- Quiz & Worksheet - Early Indian Civilization's Geography
- Quiz & Worksheet - Puritan Work Ethic
- Quiz & Worksheet - The Ancient Roman Basilica

- Sovereign Government: Definition & Overview
- Multiplying Polynomials: Examples & Overview
- Water Cycle for Kids: Activities & Games
- Introduction to Geometry Lesson Plan
- How Does LSAT Scoring Work?
- Natural Selection Lesson Plan
- Winter Science Experiments for Kids
- Inference Lesson Plan
- TExES Retake Policy
- Magnet Projects for Kids
- Cellular Respiration Lesson Plan
- Plant Life Cycle Lesson Plan

Browse by subject