Statistics Lecture 4.3: The Addition Rule for Probability

and 4.3 we talk about something called the addition rule which is great right because you're like I know how to add I'm in this class this is going to be

easy it's really about that it should make sense to us as popular stuff so let's do 4.3 before we get started in anything else I

need to tell you what something is is called when you have two or more simple events that you want to occur what that's called as a compound of that

so compound event is when you're looking to find the probability of two or more simple events okay now I'm going to give this to you

in the form of an example have you guys ever been to Vegas some people have never been to Vegas what's wrong with you I'm just kidding Vegas is this place

that's in Nevada and they do this crazy thing they're called gambling its rhythm gambling before I'm patronizing you now thirty condescending I understand but they can't learn begging sum up this

game called craps they don't play it in California but they get over there and has dice you guys ever seen or heard of

the game called craps not crappy Kratz you might never enough of that we're talking let's burn food thing in

here so I think top anyway so there's game called craps and how it's play as you roll two dice at the same time now let's bring and how you win it craps

initially is you either roll of seven or you roll an eleven and those two two numbers will double your money basically if you put it on what's called the pass

line if you don't roll a seven or 11 you can roll a two or 12 or three or any of those combinations of numbers besides the two or the twelve special cases

there you you get a point and you have to roll that number before you roll a seven again if you will seven venues so let's just keep it keep it simple gear and say if you are playing craps of the

first time if you will add seven or 11 you win are you understanding so you put five dollars down your row to seven I give you five more bucks 0:11 I give you five more bucks you will eight I take your five dollars basically

that's the basically that's the way it works there's more to it but you guys are saying the concept of the craps game so let's say that instead of rolling to die at a time you have the choice to

roll one die and then we'll other die so let's say we roll the die the first die and you get a six give you six

what two choices do you have to win still on your second die how many ways could you win okay I just said - it kind of gave that way than that what numbers

what you happen to get it or you still win so your first die I have here there's a six and you want to try to

make seven or eleven what do you have to add to this to get that one so your second die has to be a 1 that would give

you the 7 you get $5 right or you could roll it and that would give you the 11 any other choices you wouldn't be making

money you understand this one set in stone right now so we have these two so what the addition will comes down to is and what the compound events kind of let

us do there's more than one way to win this so what you want to know is what's the probability that if I roll this

second die I'm going to win basically you're not looking at just one outcome you looking at two simple events that can cause you to win are you understand the difference before was one simple

bedroo looking at just rolling a 5 or rolling a 2 now we're saying what if what if that's not all that we could have what if rolling a 1 or a 5 would

both give us a paid I don't care which one do i I don't care it's a 1 or a 4/5 them I'm getting five bucks either way so this comes up with any more probability this is where the addition

rule starts is the idea of or either one of these will satisfy our need so a compound event says what if we add the probability of rolling a 3 or a 5 that's

it I'm sorry 105 in three one four five by the way one thing in our case when we say the word or or in this case means now these are

these are mutually exclusive you can troll Bolden three and a five at the same time but there are going to be some cases where you do not have the mutually mutually exclusive component to this and

you can still be or okay we'll talk about that in just a second but or means in the context of mathematics either

this one or this one or both okay that's what more means for us either you have one or the other or both would sets by that condition now here you cannot roll both a 1 and a 5 with the same die but

we will talk about certain cases later so or means one or the other Oh

how we write out the probability is let's say we have two two events like the 1 and the 5 we would just say

probability of event a or b whenever you see that word or what that signifies to

you is the addition rule so what this means its probability of A or B this is kind of a big one okay you can't you

have to get this down the probability of A or B means in a single trial a single trial you don't do it twice you do it one time in a single trial this is the

probability of a occurring or B occurring or they both occur you understand that you don't do twice you do it one time this is a single trial I don't have your understand that this

isn't one one will die this one's overdone you know consider this one anymore okay you're just looking at one roll of die what's the probability of this or this or both that's what we mean

by or yes/no okay so probability of A or B means the probability of any single trial whether the Baker or bakery or both and

be occurring but the key part is the last part here in a single trial make sure you have that down now I just told you that 4/5 women vision is to make a whole lot in the

sense that's both a and B occurring right because you can't have both a 1 and a 5 occurring at the same time but what if I asked this question I want to

talk about the probability of being blonde or female right you fly the probability you can be blonde can't you and you can be female

can't you half of you really yes

obviously but can you be both blonde and

female yes yes kind of highlights right so so the answer is yeah we don't have this particular case when you can't take both the 1 and 5 at the same time but

you can people like blonde and female those things are not mutually exclusive and you still prefer the probability of me or either blonde or female and there's a there's overlap there

so in this case this or both thing really doesn't make a whole lot of sense but if I say find the probability of

being blonde or female well then we really don't have that mutual exclusive

context before we go any further I'd like to give you a very good example to illustrate this because I don't want to give you the addition rule and it just it's a rule for you we're going to add

something called the addition rule in just a second that's the title of our section but I'd like to kind of develop this with you so what I'm going to do let's make up kind of the condition

table for you you've been to court they're chased things you hold courts in and in them there you get just kidding yep in the court

actually like you know what you know report is right you go to the court if you do something bad or supposedly do something bad generally we're talking about in Criminal Court now so and you stand up

before the judge guy and he either condemned to you or you set you free facing so there's two options in court

either you're found guilty or you're found innocent actually you found not guilty before the successful opinion is

that kind of pessimistic also you know how innocent are you Sean not guilty we just will have enough to condemn hahaha let it done is still okay OJ Simpson you know like that ever deal so now there's

also some things that could happen if you're found guilty if you're found guilty you might have done it but is there ever cases where people are found

guilty what they didn't do it yeah they always come back like 30 years later saying oh by the way we found some DNA you actually didn't do it sorry

they're just they're use of your life which kind of sucks so you could be found guilty but you didn't actually do it

/ you're found guilty and yeah yeah you did it with the same thing at half of

innocent right claim should not if you don't do something and you're bound in so that's the way sauce work right if you if you actually did it you found innocent yelling awesome you'd be the

system I feel good probably so feel guilty I oh but you beat the system so this can actually happen so let's say that now let's throw some numbers up here so these are some I'm just making this

up as I go but let's say that this is out of a certain chord this is what has actually happened here let's talk about each of these numbers are right first number list could be 11

these people didn't do anything wrong but they were found to guilty is that the way it's supposed to work these are the ones where they come back years later maybe and say yeah we made a

mistake these people this is a mistake right and you understand this mistake if you didn't do something you didn't do it but you were found guilty in the court of law that's a bad situation being no

no one wants to be there right that's the worst someone comes your house says hey we're arresting you for this crime you go in there and they say yeah you're the one who did it when you did nothing wrong that's what these look that's what

happenes 11 people okay that happens this wood anytime you have a like a mistake it's called a false because this

is this is not what's supposed to happen right it's called a false positive they

were actually found guilty like I need to write that a little bit bigger hang on that's a false positive they were

mistakenly false mistakenly found guilty found the thing that they were looking for a port do you understand why that's a false positive they were they were connected they were actually found to be

what they were killed okay now how would this one they did it they were found guilty is that a good thing or a bad thing that's the way the courts are supposed

to work right I'm good or bad that's subjective but this is the way the court is supposed to work right if you do something bad you're punished for it you're found found guilty so this is a

I'll forgot with the with your board they using that book post positive call

I think it's a true positive take your book here I want to make sure to use the same terminology yeah let me see that it's that one some books use different different words

out when they try stick with this one this is what I thought it was a true positive means you got it right they

actually did it this one means you're making a mistake saying they actually did it this one says you got it right they actually did it you see the difference there okay now holla this one they didn't do it and they were found

innocent is that the way it's supposed to work if you didn't do something you better go in a court and say oh I found innocent this is normal because I actually didn't do something this is the

position you actually want to be it right you didn't do it you were falsely accused and are you wrongfully accused and you got out of it this is this is

good so to say true because it's working the lips - that's a true positive or negative this would be a false positive

because they got you for what this would be a false negative I'm sorry true negative truly a true you were not found guilty and you

are not comfortable so maybe I will change it to not guilty I've Illustrated even a little with them so guilty made a mistake found guilty

false positive didn't make a mistake you're found guilty that's true public did make mistake you were actually found not guilty that's a true negative you found not guilty there

the last one you did it you were just found not guilty is that the way it's supposed to work does it work sometimes sure yeah that works really I mean this happens a lot

of the top will not a lot of the times but some of the times I mean that I sit Oh Jay Simpson is kind of a joke but and that's really what happening knowing are you that guy's actually a brilliant guy because he wrote a book about it later

saying if I didn't do it I didn't do it but here's how I would have done it and just kind of stalled it out by this but anyway that's that's what he did so I

think everyone kind of a kind of can lease assumes he actually did it but he was found not guilty because of whatever they said so this is definitely false

but it's also a negative false negative they made a mistake and they didn't find them guilty so some people understand the false some true positive negatives

get alright so our question is the question can you tell me the probability

or maybe just the number for first at first find the number of the people who were guilty or did it guilty or did

let's see guilty or good let's let's look at the guilty first okay we'll look gistic guilty can you tell me how many people

appear were found guilty found guilty but if I heard some 11s and then I heard an 83 which one is it this gives you

everyone is found guilty right if some were falsely found guilty others were rightfully found guilty but altogether these are all the people who were found guilty you with Milnes so there's 83

from the guilty calm down how many people didn't do it less or did it tell me people did it what did I think that's

you guys one thing dirty clothes too did it anyway how many people did it this is

the call of digits did these people do it are they in the Didache home did this people do it did these people do it

they're in the Didache home if we go over this one more time to make sure you really graphs this okay these people they did not do it yet they were found guilty these people did it and were

found guilty these people did it but they were found not guilty these people didn't do it and they're found not guilty are you seeing this now so let's answer these questions one more time how

many people were found guilty yeah these were guilty and these were found guilty that's 83 people how many people did it or get anyone great okay these people

did it and these people did it my question is should I add this and this and then this immense to get the total people of guilty or did it but that comes down to is do you have any

crossover so if I do this if I say Oh guilty people are 11 plus 72 and did it people are 72

plus nine and I add those am I going to get above the number of people I'm looking for because I have this cross over so is this mutually exclusive is guilty and did it are guilty and did it

usually exclusive or not what do you think mutually exclusive means you cannot be in one or the other are they mutually exclusive no you can definitely be here right you can be in both the

guilty and Edyta column so these are not mutually exclusive the thing you have to watch out for in events which are not mutually exclusive is something called the double count

here if you're to find the probability which we will do we're going to find the probability of rolling a 1 or a 5 there's no way you can be both a 1 or 5

so you can't possibly double count that occurrence but here there are 72 ways you can be both guilty and did it right you can count this by 72 extra so we

have to find some way to eliminate this double count that's what the addition rule is going to do for us okay so how

many people are guilty or did it we don't have to add all four of these up because we've already counted this guy once we don't need that one so how many people are either guilty or did it or

both that's what we're asking here guilty or did it or both how many how

much 72 are guilty and did it what I'm asking for it is you're either guilty or you did it or both so if you're if you're guilty if you're in this column

you're automatically guilty right that counts that that's successfully completed our method of guilty or did it if you are here you did it you don't have to be both guilty and did it to be

in this guilty or did it number or means either or or both so if you're here if you're here do you fall in this case yes you're good if you're here you fall in

this case yeah you did if you're here you fall in this case absolutely or boat you're both of them but for more you don't need to be both just fall in one of them so let's ask the question one

more time how many people are guilty or did it or both here's guilty here's you did it here's both not just it's not just 72 it's 72 and what

which will besides 72 whales accomplishes that very good so if I add

these three numbers of 72 9 how much do I do I'm saying you guys have a little bit of a kind of hitch in your giddyup on this

so I'll go through it one more time with you all right we're trying to ask the question are you guilty or did it

you could be both these people are guilty then on that leaf on the case remember it's either or both so you don't have to be built at the same time in order to accomplish the order

remember this one do you have to roll both a 1 or a 5 see the 1 1 or 5 you can't we'll both you can't roll a 1 in 5 at the same time here you don't have to

be both guilty or did it satisfy that so I'm asking is either you're guilty or you did it or you might be go so when we look at this rule okay these people are definitely guilty they have to be on my numbers these people definitely did it

the after going numbers these people have they both guilty and it that's like a double whammy I mean they're in both spots at the same time we have to have those people that's how we're getting the 11 and the 9 and the 70 originally

if you're clear on that good all right now the question that the next question is can you find the probability of randomly selecting a person who is guilty or did it

utterly guilty or did it what we have to do is just like any other probability problem you you ever seen how many ways could you be guilty or did it over how

many total people we just surveyed or observed so can you tell me how many how many people or guilty or did it that we just talked about

remember we're not just here right it says guilty and did it we don't care for both it's going to be either or above in any of these three cases will satisfy

that that's how we got to 92 now wait a second what number goes there or if you don't know the number how would you find

that number if you add them all that's the total number of people right so if you had all of these these boxes that will give you everybody who is in that

court during that time to understand that part so let's add those up together add all these numbers up and how much is

that I take 92 divided by 177 we're going to get decimal place to the decimal to the third decimal places what

for - to 0.45 bündchen what lets you soon so we can say

52% of the people in this court or either guilty or did it that's what we

can say for this you okay for this or

for be sure the reason why we did an example that knee high on state need to be okay with this before we go any further so if there's any questions

now's the time guys we have some time so that's the time you are yeah this is the

big-deal that double count because when you have non mutually exclusive events this will happen every time in order to get rid of that double count we have

something that's called the additional so the public ARB we require some elimination of the double count

we're elimination any double-count here are what Sesame Street receive at the count what's the thing this is just the

county yeah 100 pot off if you don't get your 100 he did it twice right we all want to do that

you sound ridiculous on Sesame Street you don't be some of the Dicker's on Sesame Street do you do you know of course not you want to sound like a genius like they can always count so

this requires an elimination of McDouble count this idea right here so when we're looking at the probability of A or B it seems very easy at first because like well well look all I'm going to do is

add the people who are guilty plus the people who did it so we say sure that will work just fine probability of a plus the probability of

B that will actually work great for anything that is mutually exclusive I hope you're listening right there this will work just fine for anything that is mutually exclusive for instance

if you want to find the probability of rolling like in our last example up here a 1 or a 5 a 1 or 5 all you have to do say well what's the probability of won't

rolling in one that's 1/6 what's the problem is rolling 5 not 5/6 1/6 is one choice to make a 5 there 6006 sides so

you'd say oh yeah probably about this makes sense to you probability of rolling a 1 or 5 is 2/6 you have a 1 or a 5 there's six choices you two on the right one that means

there's been two to six that this works great for mutually exclusive events if I have something it's not mutually exclusive in this case what's going to happen here is if you

add Yogi's plus it is you're going to get this case right here and what I've crossed out is the double count here's my guilty here's one tickets notice how the same number twice you

with me so in order to eliminate the double count here's what you do you add you add this one event a that's our

killed these two event B that's our digits but then we minus the probability that they could occur together

and that's the probability a and this right here is the probability of guilty and did it notice how what I'm doing here I'm not

eliminate eliminate this altogether I'm eliminating the double count version of this you see that this one's good look at the board right now fourth this one's going to count it once this one's going

to count it twice so 1/2 times I'm taken away one time how many people understand a little more that's why that's up there so here is your event a here's your men TV here's eliminating the double promise

which says one bill I need to make before we get out of here please write down right now is we are going to have another and later on and it'll be something different right here on this

end this is in a single trial please write that down so last time we had just covered the addition rule and that was it and we found out that if we want to find the

probability of A or B occurring in a was it a single trial or multiple trials do you remember single time it's like the probability of rolling a three or a five and I run one or a five on a diet with a

single rule if we want to find that probability really it is it is addition we take the probability of the first event occurring plus the probability of the second event occurring and then we

subtract something do you remember why we have to subtract something you might get a double count if you don't have you to be exclusive events or we'll find

this word out in a second called disjoint events if you don't have that then you are going to encounter some double count so what this part does that part eliminates the double count in

this equation otherwise you're going to count the same number twice I think we saw this over here did we see this in this example I asked for the people who were guilty or did it the people who are

guilty or did it are this row is guilty this column did it but if I add this Plus this and then this Plus this I'm going to count that 72 twice and I need

to eliminate one of them so this is what we do mathematically because if I really look at this if a is guilty a is going to be 11 in 72 a is going to be 83

people if I look at B as did it these going to be 81 people but add 83 and 81 I've just counted 272 twice you with violence so this one subtraction gets

rid of that don't count making sure we only count at one time we're okay on that refresh remember last time good all right cool deal also one other thing this part gets up confusing for a

lot of people when you're talking about the addition rule you have this and up here now I'm going to preview some information we are going to get another word and the probability of a and B it's

going to mean something different than this and I that's confusing but you have to live in the context of the formula in this context we are doing how many trials one

trial so this and in this context means having a and B at the same time in the same trial does that make sense to you

now of course that can't happen when you're rolling a die once one and five are mutually exclusive events you can't roll them at the same time however you

can be both guilty and did it that's right here right that's what we're talking about here this and is the two events are happening at the same time during that single trial you see in the

future we're going to have just a standalone probability of a and B and that's going to mean the probability of doing something and then doing something

else for example for example what's the probability of rolling at three on the die and then in the next roll rolling a 5 do you see the difference there's two

things there's two successive events our student success of trials going on there that would be out of two or more trials and that's going to be the multiplication rule that you're going to see after our our tests on Monday so the

addition rule happens in a single trial just one time one roll of dice one picking out of a person just just one this and in this context stands for

still during a single trial a and B occurring at the same time during a single trial okay I also kind of threw out a

definition at your just like 20 seconds ago or so is this word called disjoint in statistics the word disjoint doesn't

mean like you have no joints just jointed statistics what it means is that the events are mutually exclusive it's really just another way to say usually

exclusive events so when you're talking about disjoint events you're talking about the events which are mutually exclusive or in other words they cannot happen at the same time that's what disjoint or mutually

exclusive means if they they're kind of synonymous for the same thing disjoint means mutually exclusive that's what we mean here so if we have something that is

disjoint or I'll say disjoint events disjoint events are events which are mutually exclusive they cannot happen at the same time cannot have at the same time that means

during your single trial here let's see if you kind of get this let me give you a verbal example here is on one single roll of the dice is rolling a 1 and a 5

usually exclusive is willing to 1 and a 5 this joint okay can the one the 5 happen at the same time now then they

are disjoint okay how about how this one you have a deck of cards you pull out one card is getting a heart and getting

a diamond disjoint the answer this question by can a heart and a diamond happen at the same time when you pull up one card member single trial then yeah these things are definitely disjoint

they can't happen the same time they are disjoint how about selecting someone this class who is female and blonde is that disjoint no there are gwon females right you can

pick someone out who is both blonde and female how about in this example is not guilty and did it not guilty and did it are those things mutually exclusive are

they disjoint or not so you can actually get someone who is both not guilty but actually did there was 90 people do that that was I seen the the definition of disjoint play out for you

this goal just means that it cannot happen in the same will die or pick up the car or same trial non disjoint means that it can so like our example with the

the blonde females or the not guilty in digits we can't show this maybe you've seen this before this is called a Venn diagram and I heard for someone that

that Venn diagrams aren't really even even taught if you don't take statistics class anymore so I have to teach you this because you're going to see this in the water places you're seeing a Venn diagram

before Jo talked about how people don't know what type of a Venn diagram is five feet up it's very easy it's not number than you looking good

so Venn diagram here's what this looks

like you shovel a box right there and inside this box from foot circles those

circles are going to represent our sets of data or sets your data your data says this would be

one event this would be another event can either overlap or not

so let's say this is the probability of a occurring and this is the probability of B occurring same thing down here probability of a occurring is in this

little ring and probability of B occurring this little disk down your same thing which one would you say would

represent sets whitsel which are disjoint the top one or the bottom one they're not joined at all right disjoint not join not join together they have no

chance of occurring at the same time how you within that so this would be a representation of a disjoint set of sense

up here we have non disjoint why are they not disjoint yep so they do connect that means there's some overlap so what

I needed to figure out is what is this little section right here what is that

little section representing if this is the probability of a and this is probability of B and this is a probability of a and this is the probability of B what's that say that

letter that's right this is a fugly anchor and all that self and probability to be occurring all by itself so is this part of it right here that it doesn't include that center section this is a

probability of a occurring all that self and B occurring all that self but this is the probability of my curry together so this would be the representation of

probability a and B happening again in a single trial the example that we can put up here this would be like what we were just talking about the probability of selecting a

person in this room who is both blonde and female there is some overlap better right there's many of you who are just female there are some of you who are

just blonde there are a few people who are both blonde and female does that make sense to you so this would be like

the blonde and female example our buffs are blonde or female examples yeah I can

smoke me now let's try that again what would feed baby kale some peas there we go so again this would be like our only female group this would be our

only blonde group and these would be the vlog females right in the middle there down here this is disjoint this would be like the example of rolling that die and

getting either a 1 or a 5 that can't happen at the same time there's no way that you're going to roll in 1 and a 5

at the same time that make that a little bit clearer for you pull it a 1 or 5 on a diet let me ask you a question though the question is

this certainly has a probability of a and B occurring what's the probability if I ask that what's the probability of

a and B for this example what's probative a and B occurring on this

example something was kind of number why did you go why did you say so why is it

zero you're right it's zero Y is zero sure in disjoint sets there is no overlap therefore that probability is sure of this there's a there's no chance of this happening right we cover Prabhu's and zero earlier on if there's

no chance of something happening you can put the probability equal to zero and that's true for this case probability of a and B there is no overlap there is no chance of those things happening at the

same time now you might be wondering why are we why we talk about that well because I don't want to give you two different formulas in the book sometimes they'll give you two different formulas for two different cases we can use the

same formula for both these cases okay either disjoint or non disjoint sets it's just whenever you become when you come across probability a and B for disjoint sets you're just going to put a

zero does that make sense to you okay so let's do a few examples and see what I'm talking about we'll talk about some complementary events after that can what I'd like to do is I want to find the probability I'm done with nail

with dice we've talked about dice too much so let's pick it let's pick cards for many day symbols and marbles I think marbles on your review is to do

something different the technicians so we want to find the probability of randomly selecting let's do let's do a

few of these examples we'll do a heart and a state oh sorry or hi said and I mean work hard for make sure you have more of their

from the standard shuffled deck of cards brother looks like a heart or a spade

from a standard deck of cards so we want

to find the probability of art or Spade that's pretty good for a spade for me

it's not bad card or Spade from our addition rule what this says is you can go directly from this and find out the information that you need from thinking about hearts and spades this says

probability of A or B once our event a in this case what's that be sure so what this says is find the probability of

event a so in a heart find the probability of event B in this case selected Spade add them together and then eliminate the double count that's what this says in English find the

public love your first event by itself find the probability of the second event by itself add them together eliminate the double count that's your overall probability now if they cannot happen together look at the board right now if

they cannot happen together I either disjoint how much is this then in that case all you're doing is adding the palm image you get it right there is

no double tell that's why this should make some sense to us that zero can take the place of that if you have disjoint sets so that one more time zero can take

the place of this you don't even need it if you have disjoint sets with it if you don't then yes you have a double count so let's go ahead and figure this one

out is drawing a heart and drawn a spade disjoint or not what do you think it can't happen save time with one trial so what we say is let's find the

probability of a heart I'll do this step by step see what's going on plus the

probability of Spade minus the

probability of the heart and the Spade they're getting worse happening at the same time during the same draw that's

what this and means in this context we're talking about a single trial so this means in a single truck you clear on that okay be very clear on that let's move it out what's the

probability of selecting a heart from a deck of cards there's more than four

hearts or I there are 13 hearts 13 hearts 13 clubs 59 inspections 50s you play more poker my goodness play Texas Holdem I taught at school you guys geez

not only heart said over I get Fletcher's all day long review this kitty yeah there's 13 hearts out of a

possible how many cards that you have to choose from plus okay so our heart the probability of just in the heart is 13 out of 52 memory signal trial so that's

of how much you have to choose from 13 hearts out of 52 total cars how about this Spade how many spades are there at an equal number for each suit so this would also be 13 out of 52

and then we'd subtract the probability of pulling out a heart and a spade at the same time what's appropriate of that happening yeah which is why in disjoint sets you don't even have to worry about

that bless you well that's not bad right if we think about this way as far as our addition rule we just have to look at the first event sick of it and the probably they occur together add them up

subtract last one how much 0.5 sure that should hopefully

make sense right there's 26 ways that you can get either a part or spayed there's 26 ways once your sources fades out of 52 total cards we know how to add fractions together you don't add the

denominators I hope oh my gosh hold on leave that alone

and then this equals 1/2 reduced fraction 26 152 is 1/2 or 0.5 if you really need your calculator to do that

I'll get in and get point 5 you really want to but that probability is 0.5 50% hopefully that wasn't a surprise to you right if we came with the deck cards and say what's the probability of getting

both fired up sir I get either a heart or Spade you're going to go to Worlds fifty-fifty there's 50% hearts there's 50% hearts and spades or skip your set diamonds and clothes it's 5050 then we

get a heart or spin you now is this classical or observed probability let's bring your X amount of stuff classical herbs or did you actually pull the card out of a deck cards then that's

classical did anyone actually pull out the car we're just thinking of it good

okay let's find the precise to do this let's find the probability of selecting a blonde or an email

so looking out in the room I'll say that when you want ones first ones Thomas you're a blonde for today welcome to the club

get you an ID card later to 18% so blonde people in the room make a point one eight of our total

proportion of our total room females how many of you there are you there's more than the males at say 60% females are 60% of you taking up this

room it's good oz I forgot it right guys just kidding how many blonde females do we have two

three four we have four so four about 12% there's only one one guy you're not even really blonde you're

pretending for today so if blondes make up 18% of our population and females make up 60% of our population implying the male's make

up to 40% you and Vaughn females are 12% let's figure out the probability a blonde female what this says is that we're going to have a by the addition rule the probability of being blonde that's our first event plus the

probability of being female that's our second event thing we're looking for - the probability that they could occur together so this would equal the

probability of blonde - the probability of being female sorry plus positive you female - and probability

blonde envy so our first event was bought blonde what's the probability that you're going to find someone who's blonde in this room

sure so point way somebody else what's the probability going to select someone who's female from this room so point six

basically she I'm right here minus the probability that they concur to can't make her together in this classroom sure we actually have several girls who are both blonde and female what's the

probability going to pick out a blonde female now why are we subtracting it again why are we subtracting that yeah because when you look at this you

automatically counted that 12% in the females you also automatically count that in the blondes right and so we need to subtract it one time to eliminate one of those counts because we've just

double countable so we add the point way to the point six zero we subtract the point 1 2 and we get how much that's it one six six what's that mean

sixty-six percent chance that you're going to randomly select left again is it a blonde female though it's a blonde or a female so give this if I

came in the room and pick the name out of the Hat there's a 66% chance and I'm going to pick any one of the women or anyone who's blonde so that would be a 66% chance I would beg you or you or you

or you or you or you or you or you were even though you have to work here right you're still so female so that doesn't I mean then you're not going happy one email here or Thomas he's not but he's

blonde so he would fit in this category you with me on this so either a female or a blonde and satisfy this this condition do you understand what I'm talking about yeah we will be pretty good about that

good for you good for you let's try one more then we'll do our complement yourself we're going to go back to a deck of cards is kind of good one for us let's find the probability of randomly

selecting out of the deck of cards a diamond or pink diamond order came in

this Kings what's everyone know we're like a pure little bit with playside

okay anyway probability selecting a diamond or King so we'll by the addition rule what this says is we're going to find the probability of selecting a

diamond all by itself then we're going to add to it the probability of selecting a key all by itself and then if they could occur together we're going to subtract the probability of selecting

a diamond and they're doing worse also one thing and a king at the same time so remember this hand this hand right here meets it during the same trap one draw

of the large okay okay all right all right what's the probability of selecting again let's suppose even this

is going to happen Sylla 13 that's right

I think so gotcha 13 over 52 see I gotta keep it

distracted by your ducky 1352 yeah there's 13 diamonds out of 52 total cards true okay let's look at the kings how many kings are there in a deck of

cards oh so the probably looks like a king is four out of what yeah please don't think I mistaken putting something like 13 there's still 52 cards right so

52 comes here as well should have a comment on it already so 13 over 52 because we have 13 times 7 52 cards for 52 because we have four kings up into

two we look at these independently just the probability of selecting a diamond just appropriately select a king and then we think of can these things happen at the same time so we didn't find the

probability of selecting a diamond and a king at the same time that can happen because you pull out one card how many choices you have for that optical there's one king of diamonds right

there's only one of them out of how many cards yeah it's not other 13 we're not talking about just the done is talking about all the cards here there's only

one diamond which is also a king out of the 52 cards how much is that going to be okay we have a common denominator that's

great you did thirteen plus four minus one that's going to give you 16 so 16 out of 52 or if you want to approximate

that you got what is decimal point three one three one one zero it's three white

our 2.30 foot three point three one zero then so about a thirty one percent chance that you're going to select either a diamond or a cane right you

don't depict just a diamond or just a king so let's think about the things that would accomplish this for us you can pick out the two diamonds that would work right you pick out the King of Diamonds or you pick out the King of

Spades or parts or anything else so any king or any diamond work work here now the last thing we're going to talk about is complimentary events I'll just take a moment to go through this

Durer that notation this is event aids is the complement of event a then bar on top mental complimented resistance

what's the probability of this what do you think one why one because they have everything it does right the event plus its complement has to be everything and

in fact if you did the addition rule probability of a grape plus the probability of the complement of a minus the probability they can occur together

at the same time what is this probability by the way this probability

of what's the probability of a and the complement of a happening at the same time in other words what's the probability you can roll a 1 and a 5 1

and a 2 3 4 5 or 6 that's not going to happen these things by definition are mutually exclusive they do not have at the same time that's not complements or

even discussed this probability is equal to 1 this one in fact equals 0 they can't happen at the same time so

really what it comes down to I gave this already which is why you go kind of looking through it if you look at this half of our equation we have the

probability of a plus the probability of the complement of a equals how much this

is all of some event and this is everything else that they could happen right what's the probability that this or anything else is going to neither

from that this implies a couple things it implies that if you have one of these events you can you can find I'm sorry that just tracked me on it he looks so

confused and it'd be nice to what your body's classroom I swear been here

before yeah anyway um I said if you go to by 13th or something if you know one

of these probabilities you automatically know the other one to see that if you know the probability of event you automatically know it's complement why treat like an equation subtract this from both sides or subtract miserable sides you're going to get two

corollaries here the probability of event a is one minus the probability of its complement occurring the probability

of a complement to event is one minus the probability of the event itself just subtract that from both sides one of those things has to happen so our

probabilities must be this way if you want to find the front event sometimes it's easier to look at the probability of a compliment that's crappy if you want the probability of the complement a lot of times it's easy to look at the

probability of event that's effective we're going to do this a lot when we get into chapter five two five does this a lot let me give you one example and we'll

call it good prevent just a basic exemple for now well I'm going to build on this as we go through our course so the probability of having a baby girl is actually not fifty-fifty I'm going to

make it up I don't know exactly what it is by that's a little bit greater 0.512 say it 0.5 1 2 now this would be

actually an observed probability because someone went out and found out how many girls that were on the whole population and determined that well maybe girls are

people on the whole population in terms that somehow it's 51.2% that you have a girl does that make sense to you so this would be considered observed probability because it came from somewhere what I

want to figure out is what's the probability of a point well without actually going out there and doing all

the work we should be able to figure this out right that the probability of having a girl is if you want point 2 percent how do we figure out the probability having a boy now mathematically we know that having a boy

is the same thing as the complement of having a girl isn't it we can't have the

same thing place usually so the probability that a boy is the probability of having a complement of a girl which is 1 minus the probability of

actually having the girl because these things are complementary events but we found out right here the probability of the complement same thing is 1 minus the probability of that event so here we go yes 1 minus the probability of actually

having a girl now I know I'm making this a lot of steps to do something that you can probably should look at it alone yet point 4 but this is how you do this in general later on which is not going to

be so so easy okay so this is this is the idea probably the boy that's the same thing it's probably the compliment the girl that's the same thing as 1 minus probability girl that's something that

we actually know and that's how you can do the point is what for a day right yeah or 48.8% chance you're going to

have a boy how people feel good about the compliment idea how whatever then we talked about does this make sense to you because have any questions on it so if you form a contain