Basic Math Organizing Possible Outcomes

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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 shirt0027

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 M0217

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 event0350

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 order0396

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 up0587

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 outcomes0600

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 one0763

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 60805

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