For more information, please see full course syllabus of Basic Math

For more information, please see full course syllabus of Basic Math

## Discussion

## Study Guides

## Practice Questions

## Download Lecture Slides

## Table of Contents

## Transcription

## Related Books

### Disjoint Events

#### Related Links

- Disjoint sets
- Probability measure
- Event
- Independence
- Dependent and independent variables
- Dependency relation

- Disjoint Events: Two events that cannot occur at the same time
- If A and B are disjoint events, then P(A and B) = 0

### Disjoint Events

B: Sam is less than 5 years old

A: John is 5 feet 10 inches

B: John is between 5 feet 5 inches and 6 feet 2 inches

A: Sam is more than 30 years old.

B: Sam is less than 12 years old

__Disjoint__: (Answers May Vary)

A: A box weighs 15 pounds

B: A box weighs less than 9 pounds

__Not Disjoint__: (Answers May Vary)

A: A box weighs more than 12 pounds

B: A box weighs less than 16 pounds

__Disjoint__: (Answers May Vary)

A: A box weighs 6 pounds

B: A box weighs less than 5 pounds

__Not Disjoint__: (Answers May Vary)

A: A box weighs more than 3 pounds

B: A box weighs less than 9 pounds

__Disjoint__: (Answers May Vary)

A: A box weighs 20 pounds

B: A box weighs more than 21 pounds

__Not Disjoint__: (Answers May Vary)

A: A box weighs more than 16 pounds

B: A box weighs less than 25 pounds

One person picks a marble from a bag of 12 marbles. Without replacing it, another person picks another marble from the same bag.

- [1/12] ×[1/11]

John recieved a 90% on his chapter 5 math test. John recieved less than 80% on his chapter 5 math test.

Kimberly rolled a number cube and got a 5. She rolled again and got a 3.

- P(5) = [1/6]
- P(3) = [1/3]

David flipped a coin and got heads. He flipped the same coin a second time and got tails.

- P(heads) = [1/2]
- P(tail) = [1/2]

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

### Disjoint Events

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

- Intro 0:00
- Disjoint Events 0:06
- Definition and Example
- Extra Example 1: Disjoint & Not Disjoint Events 3:08
- Extra Example 2: Disjoint & Not Disjoint Events 4:23
- Extra Example 3: Independent, Dependent, and Disjoint Events 6:30

### Basic Math Online Course

### Transcription: Disjoint Events

*Welcome back to Educator.com.*0000

*For the next lesson, we are going to go over two events that are disjoint.*0002

*Two events are disjoint when those two events cannot occur at the same time.*0009

*It can't happen; it is not possible.*0017

*If we have two events A and B, then the probability or the chance that both are going to occur is 0.*0020

*That means there is no chance for them to occur together.*0030

*It is as if I look at my two events, event A occurring, let's say it is that right there.*0035

*Event B occurring would be like that; they don't overlap.*0047

*That means they cannot happen together; they cannot occur at the same time.*0052

*An example of this, if I were to say that right now, it is 5 o'clock pm.*0056

*It is 5pm; let's say this is A; event A.*0075

*Event B, if I say it is early in the morning.*0083

*See how event A, this statement here, it is 5pm, and in statement B, it is early in the morning.*0102

*They cannot occur at the same time.*0110

*It is not possible for it to be 5pm and for it to be early in the morning.*0112

*These two events would be disjoint.*0118

*These are considered disjoint events because they cannot occur at the same time.*0124

*They cannot occur together.*0130

*If I were to say the same statement here, it is 5 o'clock pm.*0133

*For my second event, my second statement, I am going to say it is dinnertime.*0147

*This is possible; you can have dinner at 5 o'clock pm.*0159

*In this case, probability of A and B would be not disjoint because this can occur at the same time.*0163

*It is not disjoint.*0177

*If two events cannot occur at the same time, they are disjoint.*0180

*If they can, then it is not disjoint.*0184

*Determine if each pair of events is disjoint or not disjoint.*0189

*The first one, statement A, Samantha is more than 10 years old.*0193

*That means she could be 11, 12 years old, 13, 20, 30.*0202

*She is older than 10.*0209

*Statement B, Samantha is less than 8 years old.*0211

*She can't be older than 10 and less than 8.*0217

*This is not possible; this would be disjoint.*0221

*The second one, the first statement, John is 6 feet tall.*0231

*For B, John is between 5'10 and 6'2.*0240

*This is possible; 6 feet is between 5'10 and 6'2; this is not disjoint.*0248

*The next example, a box weighs 10 pounds.*0265

*Name a pair of events that would make this statement disjoint and another pair that is not disjoint.*0268

*We are going to create our own disjoint events and then another pair of events that would be not disjoint.*0274

*That makes sense; that could occur.*0282

*The first statement, the one that is disjoint, let's make it that statement right there.*0287

*A, my first one, a box weighs 10 pounds.*0300

*For B, our second statement, to make it disjoint, the same box weighs less than 8 pounds.*0313

*It wouldn't make sense; this is disjoint.*0332

*For not disjoint, I can say my first statement, a box weighs more than 9 pounds.*0339

*For my next statement, a box weighs less than 11 pounds.*0366

*This is true; these two statements are true; it is not disjoint.*0381

*The third example here, determine if each set of events is independent, dependent, or disjoint.*0392

*Remember independent events, when we have two events that do not affect each other.*0398

*The outcome of the second event is not affected or does not depend on the first event.*0403

*Dependent events are the opposite.*0411

*The second event is affected by the first event.*0414

*The probability of the second event occurring is affected or is determined by the outcome of the first event.*0419

*Disjoint remember is when we have two events that cannot occur at the same time.0713.2.*0429

*It is not possible for them.*0433

*The first statement, a person picks a card from a deck of playing cards.*0436

*Without replacing it, another person picks another card from the same deck.*0441

*There are 52 cards in a deck; a person picks a card.*0449

*That is the first event; the first pick is the first event.*0455

*Without replacing it, another person picks another card from the same deck.*0461

*For the first event, when you pick a card, it is 1 card out of a total of 52.*0470

*This is the first event.*0483

*Then for the second event, for the second pick,*0487

*since the first card is not replaced back into the deck, there is o1ne card missing now.*0491

*There is no longer 52 cards.*0498

*The second person is going to pick 1 card out of a total of 51.*0503

*1 card out of 52 times 1 card out of 51.*0514

*Here all we want to know is if the two events together, is it independent, dependent, or disjoint?*0518

*See how the second event here is affected by this first event because the card was not replaced.*0530

*It is not put back in; so now there is less cards.*0536

*The card that the second person picks might be different; it is affected.*0539

*This would be a dependent event; these are dependent events.*0545

*The second one, Sarah received 100 percent on her chapter five math test.*0556

*Sarah failed her chapter five math test.*0562

*The first event is that she received 100 percent.*0565

*She got an A plus; nothing wrong.*0572

*Then the second event, Sarah failed her chapter five math test.*0576

*If you get 100 percent, is that failing?--no.*0584

*This event here with this event B here cannot occur at the same time.*0588

*It is not possible for both to be true.*0597

*This would be an example of disjoint events.*0600

*The third one, Susan rolled a number cube and got a 4.*0611

*She rolled again and got a 3.*0615

*A number cube is a die; we know that there are 6 sides.*0618

*Each side has a different number; 1, 2, 3.*0626

*She rolled a number cube at got a 4.*0633

*What is the probability of rolling a 4?*0637

*Desired outcome, how many sides on this number cube is a 4?*0641

*Only 1 side; that is 1 out of a total of 6 sides.*0647

*The probability of rolling a 4 is 1/6; that is the first event.*0654

*She rolled again and got a 3; what is the probability of rolling a 3?*0660

*How many sides has a 3?--only 1 side out of 6.*0669

*Here to find the probability of rolling a 4 and then a 3 for those two events is 1/6 times 1/6.*0677

*See how even though she rolled the first time and got a 4, she rolled again.*0691

*For the second event, rolling a 3, was that affected by what she got from the first roll?*0697

*No, just because she rolled a 4 the first time doesn't mean that*0704

*she can't roll a 4 again on the second time, on the second roll.*0707

*These two events are independent.*0711

*This second roll, the second event, is not affected,*0722

*does not depend on this roll here, the probability of getting the 4.*0725

*That is it for this lesson; thank you for watching Educator.com.*0730

1 answer

Last reply by: Mary Pyo

Sat Feb 4, 2012 12:25 AM

Post by Valdo Ribeiro on December 13, 2011

Excuse my ignorance Profesor!

These are two events that cannot occur at

the same time, at the same place!?

Because it can be the same time at different places! Like 5PM in Canada and 7AM in the Philippines.