Independent and Dependent Events - Free Educational videos for Students in K-12

Independent and Dependent Events - By Anywhere Math

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00:0-1	Okay . I got my good friend , cal here
00:01	to help us out . We got two jokers cal
00:04	go ahead , take those . We've got a full
00:05	deck of cards , Right , They're all different .
00:08	Nothing special . So first he's gonna put in one
00:11	of those jokers anywhere you want . Go for it
00:14	. Next one . Just tell me when to stop
00:16	and we'll put the other one . Okay ? Put
00:19	both of them in there , just there . Random
00:21	. Right ? And we think what's the probability of
00:24	cow randomly choosing one of those jokers ? What do
00:27	you think The probability of that is almost impossible .
00:29	Almost impossible . I would agree . Right , so
00:31	cal you go ahead , tell me when to start
00:34	. Let's see . Oh the joker . Oh my
00:38	God , got it . Let's do it again .
00:40	What would be the probability if he will mix these
00:43	up again ? Put it anywhere . Are you Sorry
00:47	, go ahead and tell me again when to stop
00:49	. Stop . Okay , put it in there again
00:52	. What would be the probability of him choosing the
00:54	card again ? What do you think ? So ,
00:57	getting a joker and a joker a second time .
01:00	What do you think ? The probability ? How many
01:02	cars ? So now we've got 54 total 54 than
01:06	one 50 . Okay , but there's actually two jokers
01:11	still two out of 54 . So let's see if
01:15	he can randomly choose it again . Ready ? Tell
01:16	me when to stop . Stop there . All right
01:20	. Oh my God , it again . So welcome
01:23	to anywhere . Math . I'm Jeff , Jacobson ,
01:25	this is cow . Today we're gonna talk about independent
01:28	and dependent events . Let's get started . All right
01:49	, So today we're talking about independent versus dependent events
01:53	. So , first , let's talk about what exactly
01:55	those are . We're talking about compound events . These
01:58	are two types of compound events . So first ,
02:01	independent events are when one event does not affect the
02:06	likelihood the next event will occur . So let's kind
02:10	of talk about that in plain english , let's say
02:13	are two events were flipping a coin and rolling a
02:15	die . Now , if I flip heads , does
02:19	that change the probability of me rolling a five ?
02:23	No , right . This dye does not care what
02:27	I flip here . These are completely separate . They
02:30	are independent of one another . If I flip my
02:34	head's , it doesn't mean I'm gonna roll a six
02:37	, right ? The probability of me rolling a six
02:40	is still one out of six , no matter what
02:42	happens here , dependent events . One event does affect
02:47	the likelihood of the next event occurring . So the
02:51	probability of the next event depends on what happens .
02:55	First . Let's look at an example . All right
02:58	. Example , one find the probability of rolling a
03:00	prime number and flipping heads . So we're talking about
03:04	rolling a die and flipping heads on a coin .
03:07	Um Now if you think again , we're talking about
03:10	independent or dependent events , what would this compound event
03:14	be ? Independent ? Independent And hopefully you realize it's
03:17	independent . Like we said , these don't care what
03:20	what the other did their independent of each other .
03:22	So it's an independent event . Now for an independent
03:28	event , independent events . There's a formula we can
03:34	use for finding the probability . Now you may have
03:37	done before tree diagrams or tables to find all the
03:41	possible outcomes and and then you can find the probability
03:43	that way , but that can take a lot of
03:46	time . So instead we have a formula where the
03:48	probability of A and be that's equal to well ,
03:54	just the individual probabilities multiplied by each other . So
03:58	probability of a times probability of B . Well let's
04:04	do that . So we're finding the probability of prime
04:08	number . Mhm . And heads mike . And just
04:16	abbreviate probability of prime and Heads is going to be
04:20	equal to the probability of what was a what's that
04:24	first event ? A prime number ? What's the probability
04:27	of getting a prime number times ? The probability of
04:32	flipping hands ? Mhm . Okay . So first ,
04:37	what is the probability of getting a prime number when
04:40	you roll it die ? Well , one is not
04:43	prime two is Prime . 3's prime four . No
04:48	, that's composite . five . That is prime and
04:50	six is composite . So three Out of those six
04:55	numbers are prime . Right ? 2 , 3 and
04:59	five . What is the probability of getting a heads
05:02	? Well , one out of two . Right ,
05:04	we know that . So 36 times . One half
05:07	. Well , I can make that simplified one half
05:09	and I get 14 Here's one to try on your
05:14	own . Okay . Example to find the probability of
05:22	choosing both jokers . Now this is similar to what
05:25	we did with cow earlier except with cow when he
05:29	chose a joker , we put it back in the
05:32	deck . This time when we choose a joker ,
05:35	we're leaving it out . First . Is this independent
05:39	or dependent ? If you choose something and put it
05:41	back ? Well then it doesn't affect the next time
05:44	. But if you choose something and leave it out
05:47	, it does . So you gotta be careful with
05:49	that . So this is a dependent event . Let's
05:53	go over . 1st . The formula for a dependent
05:57	event , probability of A . And B is going
06:03	to be equal to the probability of a . Whatever
06:06	is happening . First times the probability of B .
06:10	Now this is where it's a little different . The
06:12	probability of getting be after hey , after a has
06:20	already happened . Well . First probability of A and
06:22	B . Well , I'm doing probability of in this
06:25	case a joker and another joker right ? We want
06:31	both jokers . The probability of joking and jokers so
06:33	that the probability of getting a joker times probability of
06:39	and this is getting repetitive joker after a joker has
06:45	already been chosen . Yeah . again , there's 52
06:49	normal cards in a deck . There are two jokers
06:54	. So all together there are 54 cards . So
06:59	the probability of choosing a joker the first time is
07:02	two , there's two ways to get it out of
07:06	54 total cards . Okay , now what's the probability
07:13	of getting a joker after a joker has already been
07:16	chosen ? Well , imagine that . So if we
07:19	already chose that joker , now there's only one joker
07:23	left . one way to get a joker And right
07:27	, we took a card away . So now there's
07:29	only 53 , 53 cards total . So that's the
07:35	probability of getting the next Joker . Only one out
07:38	of 53 . Because we assume we already chose one
07:41	. Okay , so now we can finish doing this
07:46	so I can simplify . That becomes one and 27
07:49	1 times one is 1 27 times 51 out of
07:56	101,431 . So the probability of getting two jokers without
08:04	replacing , which is what we just talked about one
08:07	in 1431 . Very very difficult . But if you're
08:12	wondering what cow did earlier , right . Is he
08:15	just very , very lucky . Well , probability of
08:17	getting those two jokers right ? A joker and then
08:20	another joker With replacement . Remember we put it back
08:23	in ? Well that's two out of 54 for that
08:26	first Joker , there's two jokers . 54 total .
08:29	The next Joker . It's still the same because we
08:32	replaced it . That could simplify to one and 27
08:36	same thing here . One in 27 , which equals
08:39	one in 729 . So obviously cow is very ,
08:47	very lucky . Okay , here's the last example example
08:56	three . Find the probability of choosing a heart ,
09:00	putting it back and then choosing a spade . So
09:03	here are my cards , right ? If you count
09:06	them all up , You should notice there are eight
09:10	. Now we gotta think first , is this going
09:13	to be dependent or independent ? The key phrase here
09:17	is that we put it back after we do the
09:20	first after we choose the first card . So that
09:24	should tell you things aren't changing . It's going to
09:27	be independent . The probability of choosing a heart ,
09:32	Putting it back and then choosing a spade . So
09:38	heart and spade . That's just gonna be probability of
09:42	the heart times probability of the spade . Well ,
09:46	what's the probability of choosing a heart ? Well ,
09:48	how many hearts are there ? There are one too
09:52	. Right . The probability of the heart is two
09:55	out of a total times probability of a space .
10:01	So remember if we choose a heart but we put
10:04	it back so things are changing . There's still eight
10:08	total . And how many spades are there ? Well
10:12	, if you remember these , this is a spade
10:14	here . That queen . And let's see there's two
10:19	more spades right there . I think that's all of
10:22	them . That's a club . So three out of
10:25	it . Okay , We can simplify 1 4th And
10:32	that equals three out of 32 . Okay , here's
10:35	one more to try on your own as always .
10:42	Thank you so much for watching . And if you
10:43	like this video , please subscribe . Yeah .

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