0:03 so in this lesson we are going to tackle
0:07 the concept of or probability you should
0:09 remember or probability from algebra 2
0:11 we did talk about it kind of briefly
0:14 towards the end of the class but we'll
0:16 review it here and we're gonna actually
0:18 use a new strategy that I didn't teach
0:20 you at the time which is using something
0:23 called a two-way table which we have
0:25 talked about in this class but using
0:27 tables actually makes or probabilities
0:29 very very straightforward so you'll see
0:33 how that works is we jump in now when we
0:36 do probability questions on we talk
0:39 about or and and in algebra 2 and I
0:41 didn't use these symbols with you at the
0:42 time but maybe you've seen them before
0:44 looking at geometry class or something
0:47 like that we have what's called the
0:50 intersection and the Union intersection
0:54 is this little symbol right here looks
0:57 like an upside-down U or an N and then
1:00 Union is this symbol right here which is
1:03 like a u U for union should be pretty
1:05 easy to remember intersection as like an
1:06 N in its and I think I make a note about
1:09 that at the bottom for you guys to but
1:11 you can one way you can look at these is
1:13 through a Venn diagram the intersection
1:15 of a and B is what they both have in
1:17 common the intersection of a road is
1:19 where the two roads meets so the
1:21 intersection is what they share is part
1:23 right here in green and the union when
1:25 you unite two things you put them
1:27 together and it's all of the stuff that
1:30 you see in either one of them or in both
1:33 of them so intersection works very
1:36 naturally with the concept of and in
1:40 probability you need a and B and it's
1:43 this part in the middle Union goes right
1:45 along with the concept of or probability
1:49 this or this both so Venn diagrams can
1:51 be a helpful way of visualizing this
1:54 stuff um and we'll talk about them a
1:56 little bit I personally don't care for
1:58 Venn diagrams a whole lot I'd rather use
2:00 a table but I'm gonna show you how they
2:01 works you're at least familiar with them
2:03 and there's the little hints you free
2:08 Union and for intersection so let's look
2:11 at a data set here which is looking at a
2:13 two-way table of
2:15 versus whether or not your ears are
2:18 pierced and there's a bunch going on in
2:19 this slide right here
2:21 first of all the two strategies you can
2:23 use for problems like this you've got
2:26 multiple events usually we're gonna
2:28 focus on two events at a time here we
2:30 have gender and then ear status we want
2:32 to either analyze them in a two-way
2:34 table which we've done before back in
2:37 Chapter one or in a Venn diagram
2:40 personally I like to wait tables a lot
2:42 better I find that when I make Venn
2:44 diagrams that's like think really hard
2:45 about where everything goes and I spend
2:47 too much energy just making the thing
2:49 and then even when I make it I get
2:51 confused so I like tables better but
2:53 then diagrams are perfectly good if you
2:56 like them too so what you would do the
2:57 two events that we care about in this
3:00 problem are gonna be we've our two
3:02 variables of gender and pierced ears but
3:04 our events that we're establishing our
3:08 male and pierced ears a is male B is
3:10 pierced ears so this yellow circle right
3:12 here is all the males you can see in
3:13 this problem that there are 90 of them
3:16 and they're broken into the ones who
3:18 don't have pierced ears and the ones who do
3:19 do
3:20 because B is pierced ears and these
3:23 nineteen people have both things so
3:25 they're in the middle right here then
3:26 with pierced ears if you look at these
3:27 there's a hundred three of them all together
3:28 together
3:30 there's the 19 that are male and then
3:31 there's the 18 four that are female
3:33 right here and you'll also in a Venn
3:36 diagram problem have the number where
3:38 neither of these things applies so those
3:40 are going to be females without pierced
3:42 ears evidently and that would go on the
3:44 outside of the circles and you can look
3:46 at each of these events right here the
3:49 little intersection symbol basically
3:52 means ends so this is a and B male and
3:57 pierced ears a and not B etc etc etc so
3:58 you can look at those and analyze that
4:01 then diagrams are great if you like them
4:03 but I don't care for them so I will
4:05 usually opt to make a table instead of a
4:07 Venn diagram when I analyze these sorts
4:11 of probabilities so if two events are
4:13 mutually exclusive this is our addition
4:16 rule for our probability in algebra two
4:19 I would have told you guys that or means
4:22 you add up your probabilities if they're
4:26 mutually exclusive it means that they don't
4:27 don't
4:29 overlap there's no overlap possible and
4:31 if I want to know the probability of A
4:34 or B or AP stats we'll use the Union
4:36 symbol for it see if they're kind of
4:37 interchangeable and you got to be able
4:41 to use both all you do is you add up
4:45 your probabilities and you're done like
4:46 we did in the last problem with the AP
4:49 scores three or four yeah add them
4:50 together and you're done
4:54 but a lot of times in real life events
4:56 are not mutually exclusive in other
4:59 words they overlap each other so if they
5:03 overlap what you're gonna do you still
5:04 need to add your two probabilities
5:10 together but after you do that you have
5:13 to subtract out the stuff you double
5:15 counted the stuff you double counted
5:20 would be a and the the intersection so
5:22 what this means right here is that you
5:25 have to subtract the overlap this
5:28 formula is on your formula sheets
5:30 written just like this on the first page
5:31 so you'll have that there but hopefully
5:33 this is something you can just remember
5:35 and not have to look up because we use
5:36 it quite a lot
5:38 let me quickly show you in our last
5:42 example what that we um back on my
5:44 little table right here my little bun
5:46 diagram whatever if I wanted to find the
5:49 probability of male or pierced ears I
5:51 would add up male I would add up pierced
5:54 ears but then I would be double counting
5:56 the males with pierced ears so what I
5:59 would need to do to offset that is I
6:02 would subtract out these 19 people that
6:04 I double counted because if I did all
6:06 the male's that's 9ye all the pierced
6:08 ears that's 103 that's gonna be too much
6:11 I double counted this 19 or just add
6:13 these three separate numbers which are
6:15 mutually exclusive and get your answer
6:18 generally I don't even mess around any P
6:20 stats or I would advise you not to mess
6:22 around with the formula because you can
6:24 use a table that makes the problems so
6:26 much easier so we're gonna go ahead and
6:27 I'm gonna show you guys how to set that
6:30 up so in this problem right here fresh
6:33 example we're looking at home ownership
6:35 versus whether or not you are high
6:37 school graduates so we have two events
6:39 that we care about here and they don't
6:40 define them for us I'm
6:44 go ahead put letters just so I can not
6:45 have to write out the words every single
6:47 time so G is gonna be that you're a high
6:50 school grad and then o is gonna be that
6:54 you're an owner like you own a home
6:57 so with the two-way table we're gonna
6:59 have two events and it doesn't really
7:01 matter which one goes each way I'm gonna
7:03 make grab go this way so I have high
7:06 school grad and I would have not a high
7:08 school grab a little compliment symbol
7:11 and then I would have home owner and I
7:14 would have not a home owner and then
7:16 what I'm gonna do is break the problem
7:18 up the numbers in here and put them in
7:20 the different boxes it says there's a
7:22 random sample of 500 people
7:24 the grand total usually goes bottom
7:27 right outside the box like this kind of
7:28 like a marginal distribution where you
7:30 put it on the outside and then what I'm
7:31 gonna do is start filling out the
7:33 problems with the numbers they give me
7:35 three hundred forty people were
7:37 homeowners owners this and this together
7:39 our homeowners there's three hundred
7:43 forty of them uh there are three ten
7:47 high school graduates and it says to 21
7:50 we're both homeowners and high school
7:51 graduates so the way these problems
7:53 usually work is they'll give you the
7:54 outside numbers they have to give you at
7:57 least one on the inside for the problem
7:59 to be possible so there's two hundred
8:01 twenty one that are both right here and
8:03 once you know that you can you start
8:05 subtracting things like these up to five
8:07 hundred this would be a one ninety so
8:10 you get five hundred I can do three ten
8:12 minus two twenty one and that'll get any
8:16 of that box etc so basically you just do
8:18 math no no and you can fill out the
8:22 whole inside of this picture
8:30 yeah 71 that's one nineteen yes so you
8:33 get your whole inside filled out takes a
8:35 tiny bit of effort to set up a little
8:37 two-way table but once you have it you
8:40 can answer it all sorts of probability
8:43 questions super quickly so what I'm
8:44 gonna do is leave my little table right
8:46 there and I'm a tab over to the next
8:50 page so what's the probability you're a
8:52 high school graduates
8:55 graduate was gee so you're a high school
8:57 graduate if you're here or here that's
8:58 actually just the three times and they
9:00 actually straight up told us that in the
9:01 problem so that's not very exciting
9:06 that's gonna be 310 out of 500 and you
9:08 could make that into a decimal
9:10 I think that's 62% that's not that bad
9:11 but you don't have to you can also just
9:13 leave it as a fraction
9:14 honestly AP test usually doesn't even
9:16 care if you reduce your not so don't
9:18 stress yourself too much over that
9:20 unreduced traction that's what you want
9:24 it is cool alright next problem says
9:26 that they are not a high school
9:29 graduates so not a graduate is gonna be
9:32 these guys right here and they own a
9:36 home owns a home is here so not graduate
9:39 and a home is gonna need these people in
9:42 my table so I have a hundred nineteen
9:45 people who qualify out of the five
9:47 hundred total and then you can make that
9:49 into decimal I'm not even gonna bother
9:51 with this one so we just have my answer
9:56 right there okay this next one is where
9:58 the whole table thing is actually gonna
10:00 help us because so far it's been kinda
10:01 just like looking at the picture and
10:03 it's not that difficult to do um but
10:05 with this last one here they're finally
10:09 asking us about or probability and when
10:12 they bring in or probability this is
10:14 where the two-way table kind of shines
10:17 for us so there are two events that we
10:21 care about is is I school graduate or
10:25 they own a home now you could do the
10:26 high school grads which was I think
10:29 three ten plus the homeowners which is
10:32 340 if you do that that's already over
10:35 500 and you got to subtract out the ones
10:37 you double count subtract out to 221 and
10:39 you would get your answer but if you
10:42 have a table the tables are already
10:45 separated so each box on the inside is
10:49 mutually exclusive if you're a grad and
10:51 a homeowner you're not a grad and a not
10:53 homeowner you can only fit into one of
10:55 these boxes right here so if you take
10:57 the time to make the two-way table all
11:00 you need to do is just circle up all the
11:02 stuff you care about high school grad
11:06 okay that's you that's you or OH
11:08 well I already circled that one so I'm
11:09 not gonna do that again but this is also
11:12 a homeowner right here and if you add
11:14 these guys straight up you will get your
11:17 answer for the problem always good to
11:21 show work of some fashion if you add
11:22 those up
11:29 I think that's 429 out of your 500 so if
11:30 you make a table you don't have to worry
11:32 about subtracting out the double
11:33 counting because it's separated so there
11:35 is no double counting or you can use the
11:38 formula if you prefer either way it's
11:39 kind of up to you what you do you can
11:40 even use a Venn diagram if you want to
11:45 do that so we have one more example
11:47 right here with a bunch of parts to it
11:50 fresh problem we have 60 percent of
11:51 households in the US with a landline
11:54 phone but that's gone down since 2012
11:57 and 89 percent with cell phones 51
12:00 percent have boats so our two events in
12:01 this problem that we care about Mia
12:05 L is that they own a landline and then
12:07 we all do C for cell phone doesn't
12:09 really matter what letters you choose
12:10 that's just as long as you can finance
12:13 and in my little two-way table right
12:16 here I'm gonna have L I'm gonna have not
12:19 L I'm gonna have C and I'm gonna have
12:22 not see this time they didn't give me
12:24 wrong numbers like the last one they
12:27 gave me percentages so if they give me
12:29 percentages then obviously the total is
12:31 gonna be out of a hundred percents or
12:36 one so it says sixty percent had
12:39 landlines so 60 percent landlines that
12:40 means this is already gonna be a forty
12:43 percent right here eighty-nine percent
12:47 had cell phones so 11 percent goes here
12:49 and it says the number on the inside is
12:53 that fifty one percent have both once
12:54 you know a number on the inside you just
12:56 start subtracting and doing easy math
12:58 and you just have your problem basically
13:01 and it's pretty straightforward getting
13:04 this all filled out so I've got all my
13:06 inside numbers and that took a little
13:08 bit of work in the first place to get it
13:10 all ready but once it's there it's
13:12 really easy to answer a bunch of
13:14 probabilities pretty quickly so it says
13:16 for Part B find the probability that the
13:18 household has it
13:21 one of the two kinds of phones so again
13:24 all you need to do if you took the time
13:26 to make a table is circle the stuff you
13:28 care about that could be this one or
13:30 this one those are both cell phones or
13:32 it could be this one over here so you
13:35 just add up to these three boxes or you
13:36 could also do the complement and
13:38 subtract out the one thing you don't
13:40 want however you set that up you're
13:43 gonna end up getting the answer of 98%
13:45 for this problem so it's pretty quick to
13:48 get that answer let's go on to the next
13:50 page and answer a few more quick
13:52 probabilities here I'm gonna keep my
13:56 little picture next up find the
13:57 probability that the household has
14:00 neither type of phone well actually I
14:01 just identified that in the last one
14:03 that's gonna be this box right here you
14:05 don't have a cell phone and you also
14:07 don't have a landline that's just the
14:09 simple two percents really no work to
14:12 show there to get that answer and then
14:14 finally find the probability this house
14:17 is a cell phone only when it says cell
14:20 phone only there's like that implication
14:21 there that they have a cell phone and
14:25 they also don't have a landline so that
14:27 is actually just gonna be this box cell
14:32 phone and no landline which is just 38%
14:34 so when you're dealing with more
14:36 complicated probability where it's not
14:38 just a very simple quick answer a
14:40 two-way table is a great technique for
14:42 organizing probability and making it
