Math Antics - Basic Probability - Free Educational videos for Students in K-12

Math Antics - Basic Probability - By mathantics

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00:03	Uh huh Hi , I'm rob . Welcome to Math
00:07	Antics in this video , we're going to learn about
00:09	how to do math with things that only sometimes happen
00:12	. They might be likely or unlikely . We're going
00:14	to learn about probability . Usually in Math we deal
00:18	with things that always happen the same way . They're
00:20	completely certain . Like if you add 11 you're always
00:24	going to get to . If you multiply two and
00:27	three you're always going to get six , there's no
00:29	uncertainty at all . But in the real world things
00:32	aren't always so predictable . Take a coin toss for
00:34	example , we can't predict whether it'll be heads or
00:37	tails . It's unpredictable or random and that's why some
00:41	people will flip a coin to help decide which of
00:43	two things to do . That's why I make every
00:46	decision in life . Why am I not surprised ?
00:49	Mhm Oh no . Well good luck . But even
00:57	though we don't know what each coin flip is going
00:58	to be , we do know a few things about
01:00	it . You know that with a fair coin toss
01:02	that heads is just as likely to show up his
01:05	tales . The probability of an event like getting heads
01:08	are getting tails is a value that tells us how
01:11	likely that event is to happen with our coin toss
01:15	. Since each side is just as likely and there's
01:17	only two sides to a coin . If we flipped
01:20	a coin a lot of times we should expect that
01:23	about half the flip will be heads and about half
01:25	the flips will be tails . That means that the
01:27	probability of flipping heads is the fraction one half and
01:31	the probability of flipping tales is also one half .
01:35	Let's look at this in a little more detail on
01:37	something called a probability line . It's a number line
01:40	that goes from 0-1 . A probability of zero means
01:44	that an event cannot happen . It's impossible and a
01:47	probability of one means that an event is definitely going
01:51	to happen . It's certain That's why the probability line
01:54	only goes from 0 to 1 . An event can't
01:57	be less likely than impossible and it can't be more
02:01	likely than certain . A probability of one half .
02:05	Like with our coin toss means an event is just
02:08	as likely to happen as it is to not happen
02:10	. A probability less than one half means that an
02:13	event is unlikely and a probability greater than one half
02:16	means that an event is likely . Oh and in
02:19	addition to fractions , it's also common to write probabilities
02:22	as decimals or percentages . Since you can easily convert
02:25	between those three , A probability of zero is the
02:28	same as a zero chance of something happening . A
02:31	probability of one half is the same as a 50
02:34	chance of something happening And a probability of one is
02:37	the same as 100 chance of something happening . Now
02:41	that you know how a coin toss works . Let's
02:42	see an example of an event that is unlikely using
02:45	something a little more complicated than a coin . Let's
02:48	take a look at dice . A standard die has
02:50	six sides numbered one through six when you roll it
02:54	. Any of those sides is just as likely to
02:56	come up as the others . That sounds a lot
02:59	like flipping a coin , doesn't it ? Each side
03:01	of a diet is just as likely to come up
03:03	as the others and each side of a coin was
03:05	just as likely to come up as the other .
03:07	So you might expect that the probability of rolling a
03:10	three is 50% . But remember with a coin toss
03:14	, there are only two possibilities . Heads or tails
03:17	with dice , There are six possibilities and that's going
03:20	to make a difference in its probability . One way
03:24	to think about it is that it's certain that one
03:26	of those six sides will land facing upwards which is
03:29	a probability of one or 100% . But since only
03:33	one side can face upwards for a given role ,
03:35	we have to divide up that value among all the
03:38	possibilities in the case of a coin toss . Since
03:41	there were only two possibilities , we had to divide
03:44	the probability by 21 divided by two is one half
03:48	which is the decimal 0.5 or 50% . But with
03:52	the die we need to divide the probability up evenly
03:55	between six possibilities . One divided by six is 1/6
03:59	which is equivalent to 0.167 or 16.7% . So that
04:04	would be right here on our probability line . That
04:07	means it isn't likely that I would roll a three
04:08	for instance but it's just as likely as rolling any
04:11	other number . And since all six numbers have the
04:14	same probability each number should come up about as often
04:17	as the others to see if they do . I'm
04:19	going to conduct some trials . That's an excellent argument
04:23	. Allow me to deliberate . Yeah guilty . Actually
04:31	when dealing with probability a trial which can also be
04:34	called an experiment is a process that has a random
04:37	outcome like tossing a coin or rolling dice or spinning
04:41	a spinner . And the outcome of the trial is
04:43	what happens in that particular trial like flipping heads or
04:47	rolling a three . So I'm going to conduct several
04:50	trials by rolling a die multiple times and keeping track
04:53	of how many times I roll each number . Yeah
04:59	. Yeah . Yeah . Mhm . Ha ha you
05:04	said that each number was gonna come up just as
05:06	often as the other numbers . But look there's more
05:09	twos than there are fives . How do you explain
05:11	that ? Well remember we're dealing with things that are
05:14	random . They're unpredictable . We can't know exactly what
05:18	will happen just what will happen on average . So
05:20	now I have to calculate the average . Well when
05:23	we say on average we mean that the more trials
05:26	you do , the closer you get to the expected
05:28	probabilities . Keep watching . Yeah . There now that
05:42	we've done a lot of trials you can see that
05:44	our totals are much closer to what you would expect
05:46	them to be . I guess you're probably right .
05:49	That's one of the really important things to keep in
05:51	mind about probability . If you do just a few
05:54	trials the results might not end up very close to
05:56	what you'd expect . In fact they could be way
05:58	off . But if you do more trials , you
06:01	increase your chances of reaching the expected probabilities . There's
06:04	another thing I should point out remember , the probability
06:07	of flipping heads is one half and the probability of
06:09	flipping tells is one half . The probability of rolling
06:12	a one is 1/6 and the probability of rolling any
06:15	other number on a diet is 1/6 . If you
06:18	add up the probabilities for the coin flip , you
06:20	get to over two or one and if you add
06:22	up the probabilities for rolling to die , you get
06:24	6/6 , which is also one . And that's not
06:27	just a coincidence . If you add up the probabilities
06:30	of all possible outcomes of a trial , the total
06:33	is going to be one or 100 because it is
06:36	certain that at least one of those possibilities will happen
06:40	. Let's look at some more examples for these examples
06:43	. Will use a spinner . If we had a
06:44	spinner with just six equally sized sectors , the probabilities
06:48	would be exactly the same as with dice . So
06:51	we want a few more sectors There . That's more
06:54	like it . Now . We have 16 equally sized
06:56	sectors . So what's the probability of spinning or 12
07:00	? Well , just like with dice where we had
07:03	to split up 100 between all six possibilities will do
07:07	the same thing now , but we'll split it up
07:08	between 16 possibilities . So the probability of spending 12
07:13	is 1/16 or about 6% , which is right here
07:16	on the probability line . We can see that the
07:19	probability of spending a 12 is less likely than the
07:22	probability of rolling the three . That makes sense because
07:25	there are more possible outcomes with our spinner . But
07:28	what if we color some of the sectors a different
07:30	color ? And we want to know the probability of
07:32	spending a certain color . Now we have five sectors
07:35	color blue and 11 sectors colored yellow . So what's
07:38	the probability of spending a brief remember how with the
07:41	coin toss ? We ended up with the fraction 1/2
07:44	and with the dye role we got the fraction 1/6
07:47	. In both cases we had one as the numerator
07:50	and that's because we were interested in only one of
07:53	the possible outcomes like the probability of flipping heads Or
07:57	the probability of the number three being rolled . But
08:00	in this case the top number of our fraction will
08:02	be five because any of these five sectors will give
08:05	us the color we want and the bottom number will
08:08	still be the total number of possibilities which is 16
08:11	because that's how many total sectors we have . So
08:14	the probability of spending a blue is 5/16 or about
08:18	31% . That's still considered unlikely , but it's more
08:22	likely than spending a specific number . And this method
08:25	will work for figuring out the probability of any event
08:28	. You just make a fraction with the numerator as
08:31	the number of outcomes that satisfy your requirement and the
08:34	denominator as the total number of possible outcomes . Let's
08:38	try the same method to find the probability of spending
08:41	a yellow . Our top number should be 11 because
08:43	there's 11 yellow sectors and our bottom number should still
08:46	be 16 . So the probability of spinning a yellow
08:49	is 11/16 or about 69% . Now we finally have
08:54	a probability that's considered likely . And it makes sense
08:57	because you can see by looking at our spinner that
08:59	it's more likely to spend a yellow than a blue
09:02	and you'll notice if we add up 5/16 and 11/16
09:06	, we get 16/16 or a probability of one .
09:09	So that's a good sign that we did it .
09:11	Right . Let's look at another example , suppose we
09:14	have a bag of marbles . There are three green
09:16	marbles , seven yellow marbles and one white marble .
09:19	If we mix them all up and pull out a
09:21	marble at random , what's the probability of it being
09:24	green ? Well the top number of our probability fraction
09:27	will be three because there's three green marbles . So
09:30	there's three outcomes that get us what we want and
09:33	the bottom number will be 11 . Because there is
09:35	a total of 11 possible marbles that we could pull
09:38	out . So the probability of pulling out a green
09:41	marble is 3/11 or 0.27 or 27% . It's right
09:46	here on the probability line . That means it's unlikely
09:48	. And that makes sense because you can see that
09:50	it would be less likely to pull out a green
09:52	marble than one of the other ones . Let's try
09:55	this again for calculating the probability of pulling out a
09:58	yellow marble . This time the numerator of our fraction
10:01	will be seven because there's seven yellow marbles , the
10:03	denominator will still be 11 because there's still 11 marbles
10:07	total . So the probability of point out a yellow
10:09	marble is 7/11 or 0.64 or 64% . Another example
10:15	of an event that's likely . How about pulling out
10:18	the white marble ? Well , the top number will
10:20	be one since there's only one white marble And the
10:23	bottom number is still 11 . So the probability of
10:26	point out of white marble is 1/11 or 0.09 or
10:30	9% . Not very likely . And if we add
10:34	up these probabilities we get 11/11 or 100 just as
10:38	we expected . All right . So you should have
10:41	a pretty good handle on basic probability now you just
10:44	have to remember to make a fraction with the numerator
10:47	being the number of outcomes that give you what you
10:49	want and the denominator being the total number of possibilities
10:53	. And we learned about the probability line and that
10:56	a probability can't be less than zero or greater than
10:58	one or 100% . We also learned that the more
11:02	trials or experiments you conduct , the closer your results
11:05	will get to the expected probabilities . Of course the
11:09	way to get good at it is to practice .
11:10	So be sure to do a lot of problems on
11:12	your own as always . Thanks for watching Math Antics
11:15	and I'll see you next time and I sentence you
11:18	to mhm five years hard labor learn more at Math
11:25	Antics dot com

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