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 55,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Free 5-day trial
Your next lesson will play in
10 seconds

Lesson Transcript

Instructor:
*Chad Sorrells*

Chad has taught Math for the last 9 years in Middle School. He has a M.S. in Instructional Technology and Elementary Education.

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.

A **conditional probability** is a type of dependent event. Conditional probability involves finding the probability of an event occurring based on a previous event already taking place. To calculate a conditional probability, we must use the process of dependent events because the first event will affect the outcome of the second event. Let's review the topic of dependent events to help us better understand this process.

**Dependent events** are events in which the previous attempts affect the outcome of subsequent events. Dependent events are just like they sound; each event is dependent upon what happened in the previous attempt. Let's look at an example of dependent events.

Walt has a big bag of gumballs. In his bag, he has 3 red, 6 green, 8 blue and 2 orange gumballs. What is the probability that Walt will reach into the bag and select a red gumball, then, WITHOUT REPLACING the gumball, reach into the bag and selecting another red gumball?

This probability would look like, *P*(red, without replacing and drawing another red).

We first need to find the probability of Walt selecting the first red gumball. By adding together all of the gumballs, we can see that there are 19 gumballs in the bag. There are 3 red gumballs in the bag, so the probability of getting a red gumball in the first draw is 3/19.

Next, we need to calculate the probability of Walt selecting a red gumball on his second draw. Remember, Walt did not replace the first gumball, and this will affect our totals. Walt now only has 2 red gumballs left in the bag, and the total number of gumballs is now only 18.

The probability that Walt's 2nd draw will be a red gumball is 2/18.

To calculate the probability of these two events occurring together, we would multiply the two events.

3/19 x 2/18 = 6/342

Remember that all answers must be in simplest form. 6/342 would be simplified to 1/57.

Walt has a 1/57 chance of drawing two consecutive red gumballs WITHOUT REPLACING the first gumball.

Remember, a **conditional probability** is a type of dependent event. Conditional probability involves finding the probability of an event occurring based on a previous event already taking place. The difference is that with conditional probabilities, we are just looking at the probability of one specific event occurring.

For example, thinking about Walt and his gumballs, Walt had 3 red, 6 green, 8 blue and 2 orange gumballs.

After first reaching in and selecting a red gumball, and WITHOUT REPLACING it, what is the probability that Walt's second draw will be another red gumball?

Walt knows that the probability of the first gumball being red is 3/19. Now, he has one less red gumball and one less total gumballs.

We can see that the probability of Walt's second gumball being another red would be 2/18. Remember, all fractions must be in simplest form. 2/18 would be simplified to 1/9.

The conditional probability that Walt's second gumball will be red after first drawing a red and not replacing it is 1/9.

Let's look at another example of conditional probability.

A group of teens are preparing to play a game of dodgeball. There are 30 teens that have arrived to play, 19 boys and 11 girls. What is the probability that the second player to be out is a boy after the first person out was also a boy?

We know that if the first person out is a boy, that there will only be 18 boys and 29 teens total left in the game for the 2nd round.

We can now see that the conditional probability that a boy is the second person to be out in dodgeball after the condition that a boy was the first out is 18/29. This fraction is in simplest form, so the conditional probability is 18/29.

Let's review the important facts that we need to remember when calculating a conditional probability. A **conditional probability** is a type of dependent event. Conditional probability involves finding the probability of an event occurring based on a previous event already taking place. To calculate a conditional probability, we must use the process of **dependent events** because the first event will affect the outcome of the second event. The difference is that with conditional probabilities, we are just looking for the probability of that one specific event occurring.

After viewing this video lesson, you should be able to:

- Define conditional probability
- Explain what a dependent event is and provide an example
- Calculate conditional probabilities
- Differentiate between dependent events and conditional probabilities

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 95 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
9 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
- Probability of Independent Events: The 'At Least One' Rule 5:27
- How to Calculate Simple Conditional Probabilities 5:10
- 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

- Go to Geometry

- Marketing 102: Intro to Digital Marketing
- Native Son Study Guide
- UExcel Financial Accounting: Study Guide & Test Prep
- DSST Money & Banking: Study Guide & Test Prep
- DSST Management Information Systems: Study Guide & Test Prep
- Understanding Receivables in Accounting
- Liabilities in Accounting
- Inventory Management in Accounting
- The Operating Cycle in Accounting
- Information Systems, Privacy & Security
- SBEC Technology Application Standards for Teachers
- How to Find Financial Aid for Teachers
- New Mexico State Standards for Science
- ELL Services in Massachusetts
- Publications for ESL Teachers
- WIDA Can Do Descriptors for Grades 9-12
- WV Next Generation Standards for Science

- 'The Horror! The Horror!' in Heart of Darkness
- What Is Marketing Strategy? - Examples & Objectives
- Labor Rate Variance: Definition & Formula
- The Book Thief Vocabulary
- Conditions of Freedom Essay Topics
- The Quiet American Essay Topics
- Pelvic Fracture: Complications, Treatment & Recovery
- Noun-Clause Activities & Games
- Quiz & Worksheet - Symbols & Symbolism in Orwell's 1984
- Quiz & Worksheet - Analyzing the Setting of Heart of Darkness
- Quiz & Worksheet - Understanding Multidomestic Strategy
- Quiz & Worksheet - Cult Leader Description
- Quiz & Worksheet - Configuration Management Process & Tools
- Regression & Correlation Flashcards
- Statistical Calculations for Business Flashcards

- CBEST Test: Reading Practice and Study Guide
- GACE English: Practice & Study Guide
- AP Environmental Science Syllabus Resource & Lesson Plans
- Making Legal & Ethical Business Decisions
- FTCE Marketing: Test Practice and Study Guide
- AP Music Theory Exam: Question Types
- Writing Practice: CCSS.ELA-Literacy.W.9-10.10
- Quiz & Worksheet - Behavioral Management Theory
- Quiz & Worksheet - Hersey-Blanchard's Model of Situational Leadership
- Quiz & Worksheet - Inferential Statistics for Psychology Studies
- Quiz & Worksheet - Life & Works of F. Scott Fitzgerald
- Quiz & Worksheet - Equilibrium Constant and Equilibrium Quotient

- Types of Job Redesign: Job Enrichment, Enlargement & Rotation
- The Great Wall of China Lesson for Kids: History & Facts
- ACT English Tips
- Homeschooling in Massachusetts
- NCBTMB Recertification Requirements
- What is a College Deferral Letter?
- AP World History Exam Scores
- Free GED Math Practice Test
- Dividing Fractions Lesson Plan
- How to Prep for the NYS Spanish Regents Exam
- How to Pass Math
- How to Pass the ACCUPLACER Test

Browse by subject