Probability Trees - Free Educational videos for Students in K-12

Probability Trees - By tecmath

Transcript


00:0-1	Good day , Welcome to Tech Mouth Channel . What
00:01	we're going to have to look at in this video
00:03	is just an introduction to tree diagrams and lists that
00:06	are used when doing probability . So it's gonna be
00:10	a nice , simple video . It's a second part
00:11	of a series of videos looking at probability and please
00:14	please please don't forget if you like this video ,
00:17	please hit the like button , smash the like button
00:20	and don't forget to subscribe anyway . So I'm going
00:23	to start out straight away with this so I can
00:25	do this through an example . So the example I'm
00:28	going to use is this one Okay , so a
00:31	coin is tossed two times . Okay , so it's
00:34	tossed once we get the result and it's tossed the
00:36	second time . What we're going to be looking at
00:39	with this is we're going to use a tree diagram
00:41	here to illustrate the different possible results that we can
00:44	get . And also we're going to use it to
00:46	actually work out different probabilities of outcomes . So first
00:51	off , if you throw a coin you got two
00:55	possible outcomes , you get ahead or you get a
00:58	tail and it's pretty important . First off that you
01:00	could identify the different outcomes that you can get when
01:03	drawing up a tree diagram , you've got two different
01:07	events that are occurring . So we're going to now
01:09	deal with these uh the first one And then the
01:12	2nd 1 . Now this is why they call tree
01:15	diagrams and that first event , what you could do
01:18	, Yes , we branch off here , we could
01:19	say that first event . What you can do is
01:21	you get ahead or a tail . Okay , pretty
01:26	easy . So far right for the second event ,
01:29	for the second tossing , you could've got ahead first
01:32	and then you end up with for the second toss
01:35	a head or a tail or you could have got
01:40	tails first and you could end up with a head
01:43	or a tail . So this is a tree diagram
01:46	here . Okay , nice and easy . Pretty simple
01:50	. Now look , they're a really , really good
01:51	way of organizing your thoughts when it comes to a
01:54	probability . So from this we're going to be able
01:56	to make a bit of a list and you might
01:58	be able to do this eventually without the aid of
02:00	a tree diagram . But I think it's really ,
02:02	really handy at the start to do this . So
02:04	the list that we can make up is going to
02:06	list the possible outcomes . So first off , we're
02:08	going to follow along the tree , the different branches
02:11	we get ahead then ahead . That's one of our
02:13	first possible air comes are you get ahead in the
02:17	tail ? We get a tail then ahead . Or
02:23	we could get a tail then a tail . All
02:26	right . Uh No , I say so we can
02:32	now use this to work out some different probabilities .
02:34	Okay , so I'll show you how this can be
02:36	used . Not only can we list the different results
02:39	possible is we can actually start saying now , Okay
02:42	, what's the probability say of getting two heads ?
02:46	So what's the probability getting two heads , you get
02:49	to see all together ? There are four possible outcomes
02:53	, so that's what the other bottom there , but
02:56	only one of these possible outcomes contains two head .
02:58	So to one in four chance , okay , what's
03:01	the probability of getting a head or a tail belonging
03:05	to say not in order . So it could be
03:08	a head or a tail or a tail then ahead
03:11	and that's going to give you a bit of a
03:12	head straight away . Okay , so you've got to
03:14	say tossing what's the chance of getting like a head
03:17	or a tail ? Bit nice like that , you
03:20	can say , okay , you get a head or
03:22	a tail here or a tail and a head .
03:24	So this is two , there's two Desirable outcomes out
03:28	of a total of four outcomes . Now , you're
03:31	probably looking straight away , it's okay . Probably getting
03:34	tails and tails is also one out of four year
03:36	. But what's Okay , what about the probability of
03:40	at least uh one tail ? Okay , yeah ,
03:47	you can look at this and say this is equal
03:49	to how many of these have got at least one
03:52	tail , This has at least one tail , this
03:54	has at least one tail , this has at least
03:56	one tail . So our probability is three out of
04:00	four . Okay , these are really , really simple
04:03	, right ? So hopefully you picked it up pretty
04:05	quickly , I'll tell you what I'm going to give
04:07	you an example to do with this . Okay ,
04:10	so what I'm gonna get you to do is answer
04:11	this one , a family has three Children , Boys
04:14	or girls . What's the probability of getting three boys
04:18	? What's the probability getting two girls and a boy
04:20	, But not necessarily that in order . And what's
04:23	the probability of getting at least one boy ? So
04:26	first off , what you should do is use a
04:28	tree diagram and set this up and list out your
04:31	combinations and then we'll answer these questions . So give
04:34	it a go . Okay , so let's have a
04:39	look at this . The first thing you could do
04:40	is you can say for the very first we could
04:43	end up with a boy or a girl . Okay
04:47	, that's the very very first child that's born for
04:52	the second child of sport . You can end up
04:54	with a boy or a girl or a boy or
04:57	a girl . For the third child , you could
05:00	end up with a boy or a girl , a
05:03	boy or a girl , a boy or a girl
05:07	or a boy or a girl . So that's your
05:10	tree diagram all set up . Let's list out the
05:14	problem the possibility . So you can get a boy
05:16	, boy , boy , you can get a boy
05:19	, boy , girl , you get a boy ,
05:23	girl boy , you can get a boy , girl
05:27	, girl , you get a girl , boy ,
05:30	boy , you get a girl , boy , girl
05:36	, you get a girl , girl , boy ,
05:40	or you get a girl , girl , girl .
05:43	All right , let's work out how different possibilities are
05:47	different probabilities here . So maybe you could uh see
05:52	how you go with these . If you've got up
05:54	to this stage , the probability of getting three boys
05:57	and you can see there's 12345678 possible outcomes all together
06:03	. That's a terrible , terrible eight . I'm going
06:06	to redraw that . So the probability getting three boys
06:10	, there's only one particular uh scenario where this occurs
06:15	. So there's one chance out of a possible eight
06:19	Overall Air Cubs . What about the probability getting two
06:24	girls and one boy . Now , I'm just gonna
06:27	put a little red dot . I recognize this .
06:29	Two girls and one boy . So not this one
06:33	. This has two boys were looking for two girls
06:36	. Okay , this one has two girls and one
06:37	boy . This one has two girls and one boy
06:40	. This one has two girls and one boy .
06:42	So we have 123 l with eight possibilities . Okay
06:50	, what's the probability of getting at least one boy
06:55	? So you're gonna notice all these ones here all
06:59	have at least one boy except this particular one here
07:03	. So we have 123456 seven chances out of eight
07:09	of getting at least one boy because it's only one
07:14	of these where you don't get one boy , that's
07:15	where you get three girls . So how did you
07:18	go with that ? I'll tell you what , We'll
07:19	give you one more question here . Okay for our
07:22	last example , three cards level 34 and five a
07:25	place next to each other randomly after being drawn out
07:28	of a hat . So you're going to use a
07:31	probability tree to illustrate the different results possible and they
07:35	were going to use this to work out the probability
07:38	that the number made in the three digit number made
07:40	is even or that the three digit number made is
07:43	less than 500 . So let's go and work out
07:47	a tree diagram . So the first thing you notice
07:50	is that we have possibly three different cars that we
07:54	can draw for the very first number . So we're
07:56	going to reflect this in our tree diagram , we've
07:58	got three branches coming out . That is okay ,
08:00	so the first card drawing can be a three of
08:02	four or 5 . So if you draw a 3
08:06	1st , the next card could be of four or
08:10	5 . If you draw a 4 1st , the
08:14	next card will be a three or a five .
08:18	If you were to draw a 5 1st Index card
08:21	could be of three or a four . So for
08:26	the last card drawn , if you draw a three
08:28	that are four , you're going to get a five
08:30	. If you get a 3 to 5 you're gonna
08:31	have to get the four last 43 is going to
08:34	give you a 545 is going to give you a
08:37	three 53 is going to give you a four and
08:41	54 is going to give you a three . So
08:42	we can list out all the potential results now .
08:46	We can get a 345 The double could be 354
08:52	. The W could be 435 . The W could
08:57	be 453 . The data can be 534 Or the
09:04	number could be five 43 awesome . So let's go
09:10	down and work out our our different probabilities . The
09:13	probability of getting even here , you're gonna see how
09:16	many even numbers , We'll all up . We have
09:18	six possible outcomes for our numbers and 12 of them
09:24	are even . This is a two out of six
09:28	probability . Which could be simplified Further to one out
09:33	of three probability . There the probability of getting a
09:37	number less than 500 . So what numbers we got
09:41	less than 500 year . This is less than 500
09:43	. This is less than 500 . This is less
09:45	than 500 . This is less than 500 . There's
09:47	four numbers less than 500 since the four out of
09:51	six probability , which can be simplified to two out
09:55	of three anyway . I hope that was a sub
09:59	. Help to you . Thank you to the people
10:01	who have commented to lots of people now because this
10:05	is the third time this video has been loaded up
10:07	for mistakes . Uh , so thank you for those
10:10	guys who picked out those Arizona . I hate to
10:11	have a video sitting out there with mistakes and confusing
10:13	people . So thank you for those . Really ,
10:16	really big time . Okay , if you like this
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10:50	. Uh , see you next time . Bye .

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