Basic Math Probability of an Event Not Occurring

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For the next lesson, we are going to go over how to find probability of an event not occurring.0002

We have gone over how to find the probability of an event occurring.0009

That would be the desired outcome over the total possible outcomes; it is a ratio.0014

We are comparing what we are looking for, the desired outcome,0021

over how many total possible outcomes there are, what is the total number.0025

This ratio is in the form of a fraction, top number over bottom number.0032

Probability can also be in the form of a decimal and a percent.0038

If I have probability of an event occurring, let's say it is 1/4.0043

That is a probability.0050

I can change this into a decimal and into a percent.0051

Let's just review over that.0056

To change this fraction to a decimal, I am going to take the top number and divide it to the bottom number.0058

This top number is going to go inside; the 4 on the outside.0065

Here I am going to add a decimal point.0073

I can always add a decimal point at the end of a number.0075

Then I can add 0s.0080

I can add 0s as long as it is behind the decimal point and at the end of the number.0081

Bring this decimal point up; 4 does not go into 1.0088

I am going to use one 0 to make 10.0093

4 goes into 10 twice; that is going to give me 8.0096

I am going to subtract the 10 with the 8; I get 2.0102

I can add another 0; bring that 0 down.0107

4 goes into 20 five times; that is going to give you 20.0111

Subtract it; I get 0; 1/4 is the same as 0.25.0117

You can also think of it as 1 out of 4... let's say I have 4 quarters.0129

1 out of the 4 quarters gives me 25 cents.0134

To change this to a percent, I take the decimal point.0139

I always move it to the right two spaces.0145

Think of the decimal as being small and a percent as getting larger.0149

Percents are bigger than decimals.0154

We have to move it to the right to make the number bigger.0157

I am going to move it to the right two spaces.0159

The decimal point is now going to be behind the 5.0163

Add the percent sign; that is how you change it from decimal to percent.0168

Three ways we can write probability; that is the probability of an event occurring.0174

To find the probability of an event not occurring is actually going to be 1 minus that number.0185

1, why 1?--1 is actually the biggest number we can get for probability.0196

It is like seeing the whole thing.0201

Say I have a bag of marbles.0204

In this bag of marbles, I have let's say 4 red marbles.0209

If I want to find the probability of picking a red marble,0217

probability of my event will be... I am picking a red.0223

How many red marbles do I have?--I have 4.0229

My desired outcome is 4 out of... how many total marbles do I have?--4.0233

4/4 simplifies to get 1; 1 represents the whole thing; it represents all of it.0240

The probability of something happening is 1.0251

That means it is 100 percent chance that it is going to happen.0254

That is why when you look for the probability of an event not occurring,0262

it is as if you are going to take that 1, the whole thing, and you are going to find the leftovers.0269

Back to the bag of marbles, let's say I add 2 blues.0277

I want to find the probability of picking a red.0288

I still have 4 red out of... the total number of marbles changed.0297

I now have 6 marbles.0304

Here my probability is... I can simplify this; divide each of these by 2.0306

I get 2/3; that is the probability of the red.0313

I want to find the probability of it not being red, the event not occurring.0322

The probability of not red, I am going to take the whole thing which is 1.0329

Subtract it from the event occurring, 2/3; it is like finding the leftovers.0342

From the whole thing, if I take away this much0351

which is the actual probability of the event occurring,0353

then it is like I am finding what is left over.0357

Here in order to subtract this, I need to make this the same denominator with this.0362

I can turn 1 whole into, as long as my top number and bottom number are the same, it is still 1.0371

3/3 minus 2/3.0378

I made is 3/3 because I want this denominator to be 3,0381

the same, for me to be able to subtract these fractions.0385

This becomes 1/3.0388

Another way to explain this, the probability of picking a red is 2/3.0397

The probability of not picking a red is all the rest of it which is 1/3.0407

Together the probability, it is either red or not red.0414

It is either going to be red or it is not red.0418

It is one of those two.0421

This is the probability of picking a red.0424

This is the probability of picking one that is not red.0426

Together they make up the whole thing because it is going to be one or the other.0429

The whole thing is just 1; the probability of this not occurring is 1/3.0433

The first example, we are going to use a spinner.0446

We want to find the probability of spinning or landing on a color that is not green.0448

We can do this two ways.0459

When we have something like this spinner or maybe a bag of marbles, it is a little bit easier.0462

We can make all the colors that are not green our desired outcome.0469

I can look for all of the colors that are not green.0482

I have 1, 2, 3, 4; 4 that are not green.0487

My desired outcome again is not green.0492

There is 4 of them; over total of 5.0496

The probability of not green will be 4/5.0504

The way we did it before, previous slide, it is like0509

finding the probability of actually having green and subtracting that from 1.0513

We can find the probability of green, subtract it from 1.0524

We are still going to get the same answer.0529

Here probability of picking a green, that is 1 green out of 5.0531

This will be 1 minus 1/5.0538

I can change this whole number into 5/5 to make the denominators the same.0544

5/5 minus 1/5; 5 minus 1 is 4; over... keep the denominator the same.0549

I am going to get the same answer.0562

This is obviously the easier way to do it.0566

If you can do it this way, then that is fine.0569

But you still have to understand that 1 whole would be the whole thing.0571

There is 1, 2, 3, 4, 5 out of 5; that would be 1 whole.0578

To find the probability of something not occurring would be taking the whole thing0586

and subtracting it by the actual probability of the event occurring.0589

This next one here, the probability of not red or orange.0598

Again we can just make this all the colors that are not red or orange be the desired outcome.0604

How many are not red or orange?--here is red; here is orange.0610

How many are not either of these?--I have 3.0615

My desired outcome would be all the colors that are not red or orange.0620

That is going to be my top number; that is 3; over total of 5.0625

That would be my answer.0634

But again we still have to understand that I can find the probability0636

of the red or orange and then take the whole thing, subtract it.0642

How many are red or orange?--I have 1, 2; 2 out of 5.0656

1 minus 2/5; again change this to 5/5 minus 2/5.0662

That is going to give me 3/5.0671

Given the probability of an event occurring, find the probability that the event will not occur.0683

Here probability of event A occurring is 1/4.0694

The probability of the event not occurring is 1 minus this number.0702

It is going to be 1 minus 1/4.0713

Again change this whole number; it is 1.0720

Top number and the bottom number has to be the same because I want to change this to a fraction.0724

The denominator has to be a 4; it will be 4/4 minus 1/4.0730

Again I made it 4/4 because it has to stay a 1 and the denominator has to be the same.0737

This is 4 minus 1 is 3 over 4.0744

If the probability of an event occurring is 1/4, then the probability of the event not occurring is 3/4.0752

It is like if 1 is the whole thing... 1/4, let's talk money.0759

1/4, 1 quarter out of 4 quarters.0765

If you use 1 quarter, how many quarters do you have left?0769

The remaining of it is 3 quarters; you have 3 left.0775

1/4 left over is 3/4; the rest of it is 3/4.0780

That is the probability of it not occurring.0787

Here 0.67, again 1 minus the probability of B occurring would be 1 minus 0.67.0791

Again if this is a dollar minus 67 cents, what do you have left?0811

To subtract decimals, I am going to do 1.00.0818

I am just turning this 1 into 1.00 because when you subtract decimals, you have to line up the decimal point.0823

It is going to be 1.00.0833

Again I added 0s because it is at the end of a number behind the decimal point.0835

Minus 0.67; this 0, I am going to change to a 10.0841

I borrowed it from this; that became a 9; this becomes 0.0851

It is 10 minus 7 is 3; 9 minus 6 is 3; nothing there.0860

Bring down the decimal point.0867

The probability of this not occurring is 0.33.0870

For this one, the probability of event C happening is 42 percent.0878

The chance of this occurring is 42 percent.0883

What is the chance of it not occurring?0888

This is a little bit different because it is a percent.0891

The whole thing in a percent would be 100 percent.0897

If you have a percent, then you would have to do 100 percent minus the 42 percent.0901

Or you can think of it as still 1 minus probability of C occurring.0914

Then since it is a percent, now we can change it here.0920

100 percent, we are changing this 1 whole into a percent.0924

Again decimal point at the end; move it two spaces over.0929

That is 100 percent minus 42 percent; 100 minus 42 is 58 percent.0933

The third example here, the probability of Susie passing the math test is 85 percent.0953

Find the probability of her failing the test.0960

The probability of an event occurring, which is her passing the math test, is 85 percent.0968

We have to find the probability of her failing the test.0977

It is out of a possible 100 percent.0981

We know that from 100 percent, we have to subtract0985

the percent of the probability that she is going to pass the test0994

to see what the probability of her failing the test is going to be.1001

From here, this is 15 percent.1008

This and this together have to make up the 100 percent because that is the whole thing.1013

She is either going to pass it; or she is going to fail it.1018

This is the pass; this is the fail.1020

Together they have to make up the 100 percent, the whole thing.1025

Probability of her failing the test is going to be at 15 percent.1032

The second one, the probability of Sam not picking the correct colored marble from a bag is 5/8.1041

Find the probability of him picking the correct marble.1049

The probability of Sam picking the marble, let's just say marble, the correct marble.1056

This is what they are asking for.1067

They want to know what the probability of him picking the correct marble is going to be.1068

He is either going to pick the correct marble or he is going to pick the incorrect marble.1074

The probability, what is given to us, of not picking the correct color is going to be 5/8.1086

The probability of not picking the correct marble, not correct marble, is 5/8.1095

To find the probability of actually picking the correct marble1110

is going to be 1 whole because the whole thing is 1 whole.1114

There is 8 marbles total; 8/8 is 1; 1 whole; minus 5/8.1121

Here to do this, 1 minus 5/8, I need to change this 1 into a whole number.1136

Again remember it is 8/8 because I need the denominators to be the same.1143

I have to have the top number and the bottom number be the same number for it to just be 1.1147

The denominators have to be the same; it has to be 8/8 minus 5/8.1153

See how those are the same whenever we subtract fractions; this becomes 3/8.1162

If the probability of him not picking the correct marble is 5/8,1171

then the probability of him actually picking the correct marble is going to be 3/81178

because together they have to make up 1 whole.1184

1 whole is going to be 100 percent; it is going to be all of it.1188

He is either going to pick the correct one or he is going to not pick the correct one.1192

These two numbers together have to add up to 1 whole.1198

That is it for this lesson; thank you for watching Educator.com.1202