For more information, please see full course syllabus of Statistics

For more information, please see full course syllabus of Statistics

## Discussion

## Download Lecture Slides

## Table of Contents

## Transcription

## Related Books

### Addition Rule for 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
- Roadmap
- Disjoint Events
- Meaning of 'or'
- Addition Rule for Disjoin Events
- General Addition Rule
- Generalized Addition Rule
- Example 1: Which of These are Mutually Exclusive?
- Example 2: What is the Probability that You will Have a Combination of One Heads and Two Tails?
- Example 3: Engagement Party
- Example 4: Home Owner's Insurance

- Intro 0:00
- Roadmap 0:08
- Roadmap
- Disjoint Events 0:41
- Disjoint Events
- Meaning of 'or' 2:39
- In Regular Life
- In Math/Statistics/Computer Science
- Addition Rule for Disjoin Events 3:55
- If A and B are Disjoint: P (A and B)
- If A and B are Disjoint: P (A or B)
- General Addition Rule 5:41
- General Addition Rule
- Generalized Addition Rule 8:31
- If A and B are not Disjoint: P (A or B)
- Example 1: Which of These are Mutually Exclusive? 10:50
- Example 2: What is the Probability that You will Have a Combination of One Heads and Two Tails? 12:57
- Example 3: Engagement Party 15:17
- Example 4: Home Owner's Insurance 18:30

### General Statistics Online Course

### Transcription: Addition Rule for Disjoint Events

*Hi and welcome to www.educator.com.*0000

*We are going to be talking about the addition rule for disjoints events.*0001

*First, we wanted to go over again what disjoint events mean?*0005

*and then we will talk briefly about the meaning of the word or because it has a slightly different meaning in statistics than in regular life.*0015

*Then we will talk about how to calculate the probability of a or b and that method is going to be the addition rule.*0023

*We are going to talk about the addition rule when A and B are disjoint events, as well as when they are not disjoint events.*0032

*Let us talk about disjointed events.*0041

*remember we have said before disjoint events are mutually exclusive and they cannot both happen at the same time.*0046

*so you cannot draw one card from a deck and have it be both a Jack and Ace.*0053

*It has to either be a Jack or Ace, you cannot have it be both at the same time.*0058

*Where can you select a student at random from high school and get both the junior and senior.*0065

*We have to be just one or the other.*0072

*However, you can select a card from a deck and have that it be either a jack or a heart.*0074

*they are not mutually exclusive.*0082

*They can both happen at the same time.*0085

*They do not always have to but they can.*0086

*if we wanted to draw this idea as a picture we may show these two events this is the sample space of all the possible things in the world that might happen.*0089

*Here is when A is true, your card is a Jack.*0100

*Here is when B is true, your card is an Ace.*0105

*Notice that there is no overlap between those two things.*0109

*There is no part of this space both the Jack and Ace parts are true.*0113

*In this picture we show a non disjoint events.*0118

*Here we might have as the space for all the events when jack is true but here we have the space where the card is a heart.*0123

*Here we have this space where it is both a jack and a heart.*0134

*Here we see that it is possible to be both jack and heart.*0142

*Here we might have jacks and hearts like jack of cloves or spades.*0146

*Here we have hearts that are not jacks, the king of hearts or the ace of hearts.*0155

*Now let us talk about the meaning of or.*0157

*In regular life, we usually use the word or like this, would you like soup or salad?*0163

*Would you like it to be red or blue?*0170

*Typically we mean would you like one of these things or the other one?*0173

*You cannot have both at the same time.*0179

*You can only choose one.*0181

*If you say you like this you mean to say you have to pay for the other one.*0183

*How do in math, statistics, and computer science, we are not talking about choices.*0190

*We are talking about truth values.*0196

*A or B means that either A is true or B is true, or they are both true A and B.*0199

*Basically the big idea of this is that at least one of these is true.*0211

*If both are true then you fit the world, at least one of them is true.*0219

*In that way or means slightly different in statistics lingo.*0227

*Now we could talk about how to calculate the probability of A or B and that is called the addition rule.*0233

*First let us talk about the addition rule for disjoint events.*0244

*The way you could think about this is what is the probability that you will land in this space or this space?*0247

*What is it asking you what is the probability that you will land in one of this shaded areas out of all the other possibilities?*0259

*In that way you might see that you might add together these 2 probabilities.*0273

*If A and B are disjoint, we need to first talk about what is the probability of A and B is true?*0278

*You could see that there are no points here.*0290

*There are no space, they are both A and B are covered in.*0290

*That overall space between A and B and because of that we would say 0.*0298

*There are 0 part of this space where both A and B is true.*0306

*We only have A being true or B being true but not both.*0310

*Here we have to calculate what is the probability of A or B.*0315

*You could easily see, you might want to add together probability of A and B.*0321

*This is 25% and this is 25%, maybe we have 50% likely having A or B.*0329

*That only works for disjoint events.*0338

*Here if it is disjoint events the world is simple.*0349

*If we only have one disjoint events, let us imply that same logic.*0351

*Remember we have talked about disjoint events we are asking what is the probability that you are lined within these shaded event spaces.*0357

*P(a or b) means what is the probability in one of these shaded spaces.*0367

*It is the same idea in non disjoint spaces.*0373

*I want you to watch carefully.*0378

*It is what the probability landing in A or in B.*0380

*Notice that this space is counted twice.*0386

*When you say p(a or b), what you want to know is this 8 shaped area and we do not want to count that part twice.*0391

*How can we come up with a general addition rule that will work for either non disjoint events.*0408

*You might want to start off thinking about this in the same that we did before.*0414

*First it might be helpful to add together the probability of A and B but we have counted this part twice.*0422

*It will be helpful to take one of those out.*0435

*We might subtract the probability of A and B.*0438

*In that way we can use one of these out and I will get just this area.*0444

*The reason why this is called the general addition rule is because it actually works for disjoints events as well.*0450

*Let us try for disjoint events.*0460

*We have probability of A or B, and we have probability of A + B, we will subtract the probability of A and B.*0463

*Here what is the probability of A and B?*0482

*It is 0 here.*0485

*What we are doing is adding these probabilities and subtracting 0.*0487

*That means the addition rule for disjoint events.*0499

*This general addition rule works for all events, both disjoint and non disjoint.*0503

*The general addition rule is important and very useful method of contact.*0511

*There is a different way you could write it.*0520

*I just want to briefly show that to you here.*0524

*I’m just writing down the generalize addition rule and rewrite this using slightly different notation.*0527

*Many of the frequent notation you might see is the use of union and intersection.*0538

*Union this goes to or.*0544

*When 2 countries unite, you are thinking about 2 pieces coming together and now both pieces count.*0554

*That is the picture that you should think about or.*0568

*When Alaska is united to the rest of United States together.*0571

*It is or whether here or here.*0581

*The other piece of notation you need to know is the intersection notation.*0587

*This one match perfectly to and.*0597

*The idea is where do they intersect?*0602

*Where A intersect with B?*0608

*We could just rewrite this using this notation.*0610

*This is often used for sets.*0614

*You could just use this notation.*0616

*Instead of or we can use union A and union B and that would mean the probability of A and B.*0619

*We do not have to change anything there - the probability of A intersection B.*0630

*This is just saying this whole area shaded in = p(a + b) and take out this little section.*0637

*Let us move on to some examples.*0648

*Let us say that I have chosen a person at random, which of these are mutually exclusive?*0653

*By using mutually exclusive you want to think of the same term as disjoint events.*0659

*They will be used interchangeably.*0669

*Has ridden a roller coaster or Ferris wheel, does one prevent the other from happening?*0673

*There are people who have both ridden roller coasters and Ferris wheel so I would say that these are non disjoint or not mutually exclusive.*0681

*There are nothing that prevents people from doing both.*0692

*I think I can have both songs on iTunes.*0701

*Has brown eyes has brown hair?*0708

*Here too you could have both brown eyes and brown hair or you could have just brown eyes but other colored hair.*0712

*You could just have brown hair and other colored eyes.*0720

*This is also non disjoint.*0723

*Is it left handed or right handed?*0728

*Your dominant hand is just one or the other.*0732

*I would say this is probably disjoint.*0739

*What pops into my mind right now are the ambidextrous people but even them they prefer one hand versus the other.*0745

*That is just disjoint for now.*0756

*Has had chicken pox never had chicken pox?*0760

*This one is definitely disjoint because we cannot have both have it and not at the same time.*0765

*Suppose we flip a coin 3 times what is the probability that you will have a combination of 1 head and 2 tails.*0776

*You have to remember the lessons from last time as well as the addition rule.*0786

*First we have to figure out what the entire sample space looks like.*0792

*The whole square would be, for example if we toss the coin 3 times that would mean that is 2 different power of 8.*0797

*First flip and second flip, third flip.*0811

*Half of these 8 are supposed to be heads and half of them are tails.*0816

*I am just going to start off with that.*0822

*Second one, half of these have to be heads and half have to be tails.*0824

*Half of these have to be heads and half of these have to be tails.*0834

*Same thing here.*0847

*I do not see the pattern but it is just cuts in half every single time.*0848

*The last one half of 2 alternates.*0856

*Now we know that each of these are probability of 1/8.*0862

*We can use the addition rule to figure out what is the probability that you have a combination of 1 heads and 2 tails.*0870

*We could just find other one heads and 2 tails and we add those probabilities together because these 3 things are disjoint events.*0878

*You cannot have both heads-tails-tails, and tails-head-tails at the same time nor can you have tails-tails-head at the same time either.*0894

*We have the probability of 1 heads and 2 tails = 3/8.*0904

*Ann and Bill are planning their engagement party, the room will hold 200 people so they agreed that Ann will invite 100 friends and Bill will invite 100 friends.*0916

*Everyone invited in the party showed up but only 140 people turned up, what must have happened?*0928

*It might be helpful to think about this as a picture.*0939

*Here all the people that Ann invited and here all the people that Bill invited, and together it is going to be 140 people.*0943

*There are some portions of difference that must have had overlapped.*0954

*We are trying to figure that out.*0962

*Right now we are looking at frequency instead of percentages, but obviously you can turn these to percentages if you want.*0964

*I’m just going to keep it in frequency form.*0974

*We are looking for the probability of A or B – the probability of A and B.*0976

*You can turn this probability statement into the total number of people.*0994

*We are just going to keep it as this.*1013

*We have 100 of Ann’s friends, 100 of Bill’s friends, and we do not know the overlap.*1017

*We do know that 140 people showed up eventually.*1026

*We do know that part.*1034

*The way you could do this is to divide everything by 200 because that is the total number of invited.*1036

*If we do this and we have 200 – p( a and b) I want to add this to both sides so that I can make it positive.*1048

*I am going to do that right here, 200 – 140 and that is going to be 60.*1062

*The probability of A and B are the frequency in this case of A and B is 60.*1077

*That makes sense, 60 people are here them how many people did Ann know? That is 30 people.*1084

*The same with Bill because he has invited 100 people and 60 of them knows Ann.*1096

*When you add all of these up, it makes 140.*1101

*In a community 80% of households in car insurance or homeowner insurance, 30% carry homeowner’s insurance and 50% in car insurance.*1106

*If the household is picked at random what is the probability that they are both has an insurance?*1123

*Once again we could use the general addition rule to figure this out.*1128

*Because we do not know the probability that the household owns both but we do know the probability that they either own car or home.*1133

*They at least own one and that is 80%.*1152

*40% are just home owners insurance and 50% owns just car insurance.*1159

*We want to know what is the probability that they both have insurance.*1171

*I will write the general version, it does not matter whether p of c or h comes first – the probability of C and H.*1176

*I will put in the numbers here.*1193

*I will subtract these from both sides and that gave me 10%.*1197

*10% both have insurance.*1222

*That is for the addition rule.*1224

*Thanks for using www.educator.com.*1227

0 answers

Post by Saadman Elman on June 10, 2015

Thanks it was very helpful.