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

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

### Probability of an Event Not Occurring

#### Related Links

- P(event) = (desired outcome)/(total possible outcomes)
- P(event not occurring) = 1 – P(event)

### Probability of an Event Not Occurring

P(B) = [1/5]

- 1 - P(B) =
- 1 − [1/5] =
- [5/5] − [1/5] =

P(C) = .25

- 1 - P(C) =
- 1 - .25 =

P(G) = .47

- 1 - P(G) =
- 1 - .47 =

P(A) = 67%

- 1 - P(A) =
- 100 - 67 =

P(B) = 6.5%

- 1 - P(B) =
- 100 - 6.5 =

- 100% - 95%

- 100% - 55%

- 100% - 82.5%

- P(not correct marble) = [6/11]
- P(correct marble) = 1 - P(not correct marble)
- P(correct marble) = 1 - [6/11]
- P(correct marble) = [11/11] − [6/11]

- P(not correct marble) = [4/13]
- P(correct marble) = 1 - P(not correct marble)
- P(correct marble) = 1 - [4/13]
- P(correct marble) = [13/13] − [4/13]

*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

### Probability of an Event Not Occurring

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
- Event Not Occurring 0:07
- Formula and Example
- Extra Example 1: Use the Spinner to Find Each Probability 7:24
- Extra Example 2: Probability of Event Not Occurring 11:21
- Extra Example 3: Probability of Event Not Occurring 15:51

### Basic Math Online Course

### Transcription: Probability of an Event Not Occurring

*Welcome back to Educator.com.*0000

*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 much*0351

*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 like*0509

*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 thing*0586

*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 probability*0636

*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 subtract*0985

*the percent of the probability that she is going to pass the test*0994

*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 marble*1110

*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 3/8*1178

*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

0 answers

Post by Beatriz Zmuda on September 30, 2014

Thanks

2 answers

Last reply by: Ruby Zhang

Wed Jun 14, 2017 10:48 PM

Post by GLENN MENSAH on May 12, 2014

i also dont get extra example 3

1 answer

Last reply by: Firebird wang

Wed Oct 12, 2016 10:49 PM

Post by Jaish Mishra on May 12, 2013

I don't really get extra example 3