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

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

### Organizing Possible Outcomes

#### Related Links

- Compound events: When there are two or more different events that will affect the possible outcomes
- Fundamental Counting Principle: If one event has
*m*possible outcomes and a second independent event has*n*possible outcomes, then the total possible outcomes for both events together is*m*×*n*

### Organizing Possible Outcomes

June, San Jose,

June, San Diego

July, Los Angeles

July, San Jose

July, San Diego

October, California

November, New York

November, California

December, New York

December, California

Steak sandwhich on wheat bread

Fish sandwhich on white bread

Fish sandwhich on wheat bread

Club sandwhich on white bread

Club sandwhich on wheat bread

Cheese sandwhich on wheat bread

Pork sandwhich on white bread

Pork sandwhich on wheat bread

Steak salad with thousand island

Chicken salad with ranch

Chicken salad with thousand island

Fish salad with ranch

Fish salad with thousand island

Vanilla, medium

Vanilla, large

Strawberry, small

Strawberry, medium

Strawberry, large

Mango, small

Mango, medium

Mango, large

Chocolate, small

Chocolate, medium

Chocolate, large

Oreo, medium

Orange, small

Orange, medium

- 6 ×6

- 6×6 ×6 ×6

*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

### Organizing Possible Outcomes

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
- Compound Events 0:08
- Compound Events
- Fundamental Counting Principle
- Extra Example 1: Create a List of All the Possible Outcomes 4:47
- Extra Example 2: Create a Tree Diagram For All the Possible Outcomes 6:34
- Extra Example 3: Create a Tree Diagram For All the Possible Outcomes 10:00
- Extra Example 4: Fundamental Counting Principle 12:41

### Basic Math Online Course

### Transcription: Organizing Possible Outcomes

*Welcome back to Educator.com.*0000

*For the next lesson, we are going to go over organizing possible outcomes using compound events.*0002

*A compound event is when you have two or more different events that will affect the possible outcome.*0010

*When you have different options, that is going to affect the actual outcome.*0018

*An example is say we want to pair up the type of shirt*0027

*that we are going to wear with the type of pants we are going to wear.*0033

*My two events is going to be my top, my shirt, with my bottom.*0037

*Let's say my options for my shirt.*0050

*Say I am debating on whether I should wear a t-shirt or a collar shirt.*0053

*For the bottom, let's say I am either going to pair it up with a skirt or say pants or shorts.*0065

*My two events are the shirt and the bottom.*0082

*You are going to pair them up.*0089

*The different pairs are going to create the different possible outcomes.*0091

*When you list out all the possible outcomes, that is here.*0096

*That is what you are doing; you are creating the organized list.*0101

*If I say t-shirt with skirt, t-shirt with pants, t-shirt with shorts.*0105

*If I list them all out, that is a way for you to just list out all the possible outcomes using a list.*0110

*The next one, drawing the tree diagram.*0120

*When you draw the tree diagram, you are going to first list out the first event.*0123

*That would be the shirt.*0128

*You are going to do t-shirt with the collar.*0132

*Those are your two options for the first event.*0142

*Then you are going to branch out from the t-shirt.*0148

*How many options do I have to pair up with this?*0152

*I have three; you are going to do one, two, three.*0154

*You are going to write the skirt here; pants; and shorts.*0160

*Same thing with this.*0169

*It is going to be the skirt with the pants with the shorts.*0172

*Skirt, pants, and then shorts.*0180

*The t-shirt with the skirt is one option.*0185

*T-shirt with the pants; and then t-shirt with the shorts.*0192

*Then collar shirt with the skirt; collar shirt with the pants.*0198

*And then collar shirt with the shorts; would be your other options.*0203

*Total, we have six possible outcomes; that is the tree diagram.*0207

*The fundamental counting principle is when you just take all the possible outcomes for this first event M*0217

*and then all the options for your second event N and you multiply them together, M times N.*0229

*You are going to get the total possible number of outcomes.*0241

*M, let's say M in our example is the type of shirt that we have, the options.*0245

*We have two; M is 2; that is the first event; M is 2.*0252

*Our second event is type of skirts, pants, bottoms, whatever we are going to wear.*0259

*That is N; how many options do we have there?*0265

*We have three; N is 3.*0267

*We multiply them together; we are going to get 6.*0271

*I know that I have 6 possible outcomes total.*0277

*That is the fundamental counting principle.*0282

*Let's do some more examples.*0287

*The Jackson family plans to travel in July or August to San Francisco, San Jose, or San Diego.*0290

*Create a list of all the possible outcomes.*0297

*We have two events. The first event is going to be when the family is going to travel, July or August.*0300

*That is the first event.*0307

*The second event that is going to affect the outcome will be the place; where.*0309

*Let's see... I am just going to create a list of all the possible outcomes.*0318

*My possible outcomes can be in July to where?--San Francisco.*0324

*July to San Jose; and then July to San Diego.*0336

*It is easiest when you have to list them out, to list out the first event*0350

*and then the different possible places in your second event.*0356

*See how this is the first option for event one.*0361

*The second one will be August to San Francisco.*0367

*August to San Jose; and then August to San Diego.*0375

*We have six possible outcomes.*0389

*For this example, Samantha cannot decide if she is going to order*0396

*chicken sandwich, turkey sandwich, or a club sandwich on either white or wheat bread.*0403

*Create a tree diagram that lists out all the possible outcomes.*0408

*The first event, the first option, is the type of sandwich.*0412

*The second event is going to be the type of bread.*0426

*The first part of doing this is to figure out your events, the different things,*0435

*the different events that are going to affect your outcome, the sandwich and then the bread.*0443

*For the first event, I am going to list it out.*0449

*Again I am drawing the tree diagram.*0451

*The first event is going to be between chicken...*0453

*Give yourself some space between each... turkey, and the club.*0460

*Then I am going to branch out from chicken.*0472

*What are the possible types of bread on the chicken?*0479

*It is going to be white or wheat; for the turkey, white, wheat.*0483

*On the club, we can get the club with white or wheat.*0498

*The chicken with the white, that is one option.*0506

*I can just say this is the white; the chicken with the wheat.*0515

*The turkey with the white; turkey with the wheat.*0531

*Club with the white; and club with the wheat.*0540

*See how you went from chicken to white, chicken to wheat,*0550

*turkey to white, turkey to wheat, club to white, and club to wheat.*0554

*Those are all of your possible outcomes here.*0558

*You can also make your bread your first event and then your sandwich the second event.*0565

*You would just do white and wheat; you list those two out.*0572

*Then you would branch out to the three options for the sandwich.*0578

*It works either way.*0583

*It doesn't matter which one you label as your first event and your second event.*0584

*As long as you make sure that you are going to pair up*0587

*each of the first events with each option for the second event.*0590

*You have six different options.*0596

*The next one, draw a tree diagram showing the possible outcomes*0600

*for the choice of vanilla, strawberry, chocolate yogurt in a small, medium, or large cup.*0604

*First event is going to be the yogurt.*0612

*The second event is going to be the size, type of cup.*0620

*Yogurt is going to be either vanilla, strawberry, or chocolate.*0628

*You can get the vanilla yogurt in small, medium, or large.*0646

*You can get the strawberry in small medium or large.*0657

*You can order the chocolate yogurt in small, medium, or large.*0664

*The different possible outcomes is going to be vanilla to the small; small vanilla.*0671

*Or you can just do vanilla small; vanilla medium; vanilla yogurt in a large cup.*0678

*Or strawberry small; strawberry medium; strawberry large.*0687

*Then chocolate small; chocolate medium; and chocolate large.*0697

*These will be your possible outcomes.*0702

*We have one, two, three, four, five, six, seven, eight, nine.*0705

*Remember the fundamental counting principle.*0713

*We have M as our first event and N as your second event.*0716

*If this is M, this is N, how many options do we have for our M?*0725

*We have three different options for the yogurt.*0729

*If we were to do M times N, we have three options for our yogurt, that is 3.*0734

*Times how many options do we have for the size?*0740

*Small, medium, large; we have 3; N is 3.*0743

*To find the total possible number of outcomes, it is going to be 9.*0748

*3 times 3; 9; we have all 9 here.*0753

*Three, four, five, six, seven, eight, and nine.*0756

*We are going to use that fundamental counting principle again for this one*0763

*to find the total possible outcomes for rolling a number cube three times.*0767

*We have three different events.*0775

*Just the three different times you are going to be rolling the number cube.*0778

*Let's say a number cube... we are going to say first.*0786

*Because it is going to be rolled three times.*0791

*The first time, the second time, and the third time.*0792

*The first time we roll it, how many different options are there?*0800

*How many different possible outcomes for just that first time you roll the number cube is going to be 6*0805

*because the number cube has 6 sides and each side has a different number.*0812

*We have 6 different possible numbers that can show up within our first roll.*0817

*Within the second roll, how many options do we have there?--we also have 6.*0825

*Then for the third, we also have another 6 because there is 6 different numbers.*0834

*To find the possible number of outcomes, we know that we have to do M times N.*0842

*That is if you have two events.*0852

*In this case, we have three events; we just multiply all three together.*0854

*We can just label this as M, this as N, and the third one whatever you want, P.*0859

*We are going to do times P.*0867

*That is going to be 6 times the 6; 6 times 6 is 36.*0871

*Then we are going to multiply this by 6.*0880

*This is 36; 6 times 3 is 18; 21.*0888

*There are 216 different possible outcomes when you roll the number cube three times.*0895

*Just to list out a couple, the first time you roll it, you can roll a 2.*0907

*The second time you roll it, you can roll a 1.*0913

*The third time you roll it, you can roll let's say a 1.*0916

*That is just one of the 216 different possible outcomes; my answer is 216.*0921

*That is it for this lesson; thank you for watching Educator.com.*0933

0 answers

Post by Rafael Wang on August 29 at 04:07:59 AM

you spelled san francisco wrong