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:
*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.

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.

**Independent events** are events that do not affect the outcome of subsequent events. In an independent event, each situation is separate from previous events. An example of independent events would be the probability that it will rain on Monday, and the probability of getting an A on my next test. These two events are independent of each other. The chances that it will rain on Monday does not affect the score on my next test. To calculate the probability of multiple independent events, find the probability of each event happening separately and multiply them together.

Occasionally when calculating independent events, it is only important that the event occurs at least once. This is referred to as the **'At Least One' Rule**. To calculate the probability of an event occurring at least once, it will be the complement of the event never occurring. This means that the probability of the event never occurring and the probability of the event occurring at least once will equal one, or a 100% chance.

For example, the probability of winning the grand prize in a local drawing is 1 out of 30. Tim and his wife, Jane, both bought tickets. What is the probability that at least one of them will win the grand prize? We first need to find the probability of Tim and Jane not winning the grand prize. Since the probability of one person winning the prize is 1 out of 30, the probability of one person not winning the grand prize is 29/30, or 0.96.

Remember, to calculate the probability of multiple independent events - in this case, both of them not winning the grand prize - we find the probability of each event happening separately and multiply them together. Since both Tim and Jane have the same probability of not winning, we will need to square the probability of one not winning. So, 0.967^2 = 0.935.

So, the probability that neither Tim nor Jane will win the grand prize is 0.935. To calculate the probability of at least one of them winning the grand prize, we need to find the complement of that number. The probability of not winning plus the probability of at least one winning is going to equal one whole. So, by subtracting 1 - 0.935, we can see that the probability of either Tim or Jane winning the grand prize is 0.065, or a 6.5% chance.

As the announcer steps to the mic to call out the winning ticket, Tim and Jane do not like their chances. The announcer steps to the mic and calls out the name Jane. Jane is so excited and jumps with joy that she has beaten the odds to win the grand prize.

Let's look at another example. Tim and Jane are planning to use their grand prize winnings to take a four-day ski trip. They want to make sure that it will snow at least one day while they're on their trip. The ski resort that they booked with says that there is a 65% chance that it will snow each day. What is the probability that it will snow at least one day while on their four-day ski trip?

The first step to calculate the chance of it snowing at least one day is to find the probability of it not snowing during their four-day trip. The resort says that there is a 65%, or 0.65 chance of it snowing each day. To find the probability of it not snowing, we will need to subtract 1 - 0.65, which equals 0.35. So the probability of it not snowing on any given day is 0.35.

Since they are going to be there for four days, we will need to multiply 0.35 times itself four times to represent the chance of it not snowing at all. The easiest way to do this is by using exponents. We will need to calculate 0.35^4, which is 0.015. The probability that it will not snow at all over their four-day trip is 0.015.

To calculate the probability that it will snow at least one day, we need to calculate the complement of this event. To do so, we will subtract 1 - 0.015, which equals 0.985. Tim and Jane know that there is 0.985, or 98.5% chance that it will snow at least one day during their ski trip. As Tim and Jane arrive at the ski resort, snow begins to fall. It is the most beautiful sight they've ever seen.

So, to review, **independent events** are events that do not affect the outcome of subsequent events. In an independent event, each situation is separate from previous events. Occasionally when calculating independent events, it is only important that the event occurs at least once. This is referred to as the **'At Least One' Rule**. To calculate the probability of an event occurring at least once, it will be the complement of the probability of the event never occurring. When calculating this amount, you can use exponents to multiply the amount of the events that occurred.

After watching this lesson, you should be able to interpret the process of complementary events to find out the probability of something happening at least once.

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
8 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
- 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

- AP Chemistry Syllabus Resource & Lesson Plans
- Earth Science: High School
- Common Core ELA - Literature Grades 11-12: Standards
- Psychology 102: Educational Psychology
- US History to Reconstruction for Teachers: Professional Development
- Technology in the Classroom: Help & Review
- AEPA Middle Grades Math: Introduction to Fractions
- Quiz & Worksheet - Hearing Impairment Characteristics & Treatment
- Quiz & Worksheet - Giftedness in Children
- Quiz & Worksheet - Characteristics of a Blind Study
- Quiz & Worksheet - Structures & Functions of the Middle Ear
- Quiz & Worksheet - Visual Intelligence

- What is a Cognitive Interview? - Questions, Techniques & Evaluation
- Cauchy-Riemann Equations: Definition & Examples
- High School Interview Questions & Tips
- Books for Teaching All About Me
- Excelsior College BS in Business Degree Plan Using Study.com
- Music Word Walls
- Reading Activities for Kids
- Preschool Book List
- Kindergarten Word Walls: Ideas & Activities
- Behavior Rubric Examples
- The Butter Battle Book Lesson Plan
- How to Pass Calculus

Browse by subject