>> Hi, this is Julie Harland
and I'm YourMathGal.
Please visit my website
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[ Silence ]
This is part 3
of Survey Problems
where we can use Venn diagrams
to answer some questions
about a survey.
So in this video,
we'll learn how
to create a Venn diagram
to store information
from a survey
so that we could answer other
questions about the survey.
Here's our first problem.
A survey of 100 students was
taken to determine how many
were gluten free
and how many were
lactose intolerant.
28 were gluten free,
35 were lactose intolerant,
and 10 were both gluten free
and lactose intolerant.
How many students were neither
gluten free nor
lactose intolerant?
In other words,
they didn't have either
of those problems.
So we're talking
about 2 different things,
gluten free
and lactose intolerance.
So let's make a Venn diagram
that has 2 circles in it,
one for gluten free and one
for lactose intolerant.
How about I call this one the
GF for gluten free
and this one lactose
intolerant, I'll put LI?
You just could label it
however you want.
The Venn diagram is so that
to help you answer
the question.
All right, so now let's look
at the information
that was given--
that was given to us.
28 were gluten free, right?
Well, if we look
at gluten free,
we know that there are 2
regions here.
Notice that there are
2 regions?
So if 28 were gluten free,
we don't know how--
you know, where to put
that exactly.
Like I can't just say 28 right
here because that's a assuming
that all 28 were gluten free,
right?
And not lactose intolerant,
but we don't know that.
So we can't fill in how
that works like another
where it's just a 20 and 8,
how does it go?
We're not sure.
25 are lactose intolerant--
35 were lactose intolerant.
Same problem.
There are 2 region here--
2 regions here,
the numbers have
to add up to 35.
So I can't fill anything else
out in here yet.
Okay, let's see
if I can get some place.
10 were both gluten free
and lactose intolerant.
Yes, so I'm going to--
after I'm able to use
that information,
I'm going to actually write
down and use it.
10-- all right,
I know where the 10 goes,
the 10 is going
to go right there.
Okay, now we can go back up
and see if we could fill
in something else.
28 were gluten free.
Well, now I know
that these 2 regions are
where the gluten free is,
together must add up to 28.
All right,
so if 10 of the people are
in this part, how many have
to be over in this part
over here?
Well, 28 total, 28 minus 10,
this is got to be 18.
I've now used that piece
of information.
Okay, let's keep going.
Can I do anything with this 35
for lactose intolerant?
Okay, remember,
this is the circle,
the 2 regions with the people
that are lactose intolerant,
and so these 2 regions
together, the numbers have
to add up to 35.
All right, well,
so I've got 10 in here
so what goes over here?
These together have to add
up to 35 so there must be 25
over here.
So these are the people
that are only lactose
intolerant, right?
That 10 plus 35 is the--
all of the people
that are lactose intolerant
including these 10
that are both gluten free
and lactose intolerant.
Most common mistake is
for people who've got 35 right
over here where I have written
25 or 28 over here right
at lactose--
I'm sorry gluten free,
so we've used this piece
of information.
Now, is there anything else
given here
if you read the
question again?
The survey of 100 students.
So all together,
notice there are 4 regions
here, 1, 2, 3, 4.
I haven't said what's
out here, all together,
these numbers have to add up.
All 4 numbers have to add
up to 100.
So let's see what it adds
up to you so far.
I've got 18, 10, and 25.
So, so far I've got 18, 10,
and 25 so that's 53 so far
and so 53 plus what will give
me 100?
Or you could just do 100 minus
53 if you don't know how
to do it in a different way.
So there must be 47 people
who are neither gluten free
or lactose intolerant.
So here's a peop--
there's a group of people
where a lot
of people have digestion
problems, basically.
So now we've got a picture,
right, of our Venn diagram.
And now we could answer this
question, how many students
were neither gluten free nor
lactose intolerant?
What are we talking about?
That's the people out here
on the outside,
that's what we want.
We're looking
for that number of 47.
So the answer
to this problem is 47.
Kind of tricky.
So this would be just 2,
right?
2 kinds of things going on.
So we're going to do another
with 2 things going on
and then we'll make a separate
video, what
if there's 3 things going,
it does get more complicated,
that-- just slowly work
through it
and you shouldn't have too
much trouble.
Read carefully,
sometimes you just can't fill
in the number and you have
to go back to it later.
So what I do is I
like to either circle it
or something
so I know once I've used
that piece of information,
I'm looking
for some other piece
of information to add another,
you know, number somewhere
in this Venn diagram.
[ Pause ]
So here's our next problem.
In a group of women,
25 had red hair,
25 had green eyes
but not red hair,
13 had red hair
but not green eyes,
and 63 did not have
green eyes.
How many women were
in that green?
First thing,
you can't just add 25, 25, 13,
and 63, okay?
So when you see all the
numbers, you could just can't
add them all up.
For instance,
if I said that 100 people said
they had cats,
100 people had dogs
in some survey,
you can't assume there're 200
people because maybe that's
the same 100 people,
maybe there are people
that have both cats and dogs,
so be careful.
So see if you could make a
Venn diagram.
Now, there're really 2 things
we're talking about here,
right, green eyes
and red hair.
So the key is
to draw a Venn diagram,
how about I do G
for green eyes and R
for red hair.
So see if you could go ahead
and fill in the numbers
and figure out the answer
on your own first.
Okay, let's see,
in a group of women,
let's see what we could
fill in.
25 had red hair, okay,
so if we look at the circle,
the set of people
with red hair,
there're 2 regions here.
So I can't use
that information yet,
I can't fill
in that 25 'cause does it go
10 and 15, you know,
how does it go?
Is it all 25 over here?
None of them had green eyes?
We don't know
so you can't use that.
25 had green eyes
but not red hair, okay?
Now what region would that be?
They've got green eyes
so they're
in the green circle here
but they don't have red hair.
So they can't be
over in this intersection.
So that can't be filled
in right now.
25 had green eyes
but not red hair.
That would be this region
over here.
These are the people
that only had green eyes,
right?
But they're not in the circle
where they also had red hair.
Next one, 13 had red hair
but not green eyes.
So okay, so where is that?
Can we fill that in?
Well, here are all the people
that had red hair, right?
This whole part here
and if you had red hair
but not green eyes,
you're only
in this little region
over here so I could do
that as well.
That's only
in that little piece
right here.
Let's see,
we could either go back up
and see if we could fill
in this-- where this 25 split
set now or we could keep
on going to see
if we could do it and go
to the 63, right?
It doesn't matter 'cause I'm
not sure which one I have
to do first
or maybe it doesn't matter.
So let's just keep going.
63 did not have green eyes.
Okay, so here, this circle
for the G, are all the women
that had green eyes.
So I know outside
of that circle has
to add up to 63.
And what's outside
of this circle is this region
plus that region so together,
the people out here, right,
that don't have either green
eyes or red hair,
plus the 13 have to add up 63.
So if this is 13,
what is this going to be
over here?
50 in order to add up 63.
So I was able to use
that piece of information.
Now, let's go back up through
at the beginning to see
if there is another piece
of information we haven't
used yet.
25 had red hair.
Okay, so now we can go back
up to the red hair
and here is the whole circle,
R for red hair,
so together these 2 pieces
here have to add up to 25
and if this is 13,
what's going to be in here?
12 to add up.
Now, I've filled
in all 4 pieces, right?
All 4 regions
in this Venn diagram
so I can answer how many women
are on the group
like adding those 4 numbers.
So what happens
when we add those 4 numbers?
We have 50, 25, 12, and 13,
I've got 100.
So there are 100 people
in the group.
Now, I could've asked a
different question,
I could've said let's see,
how many have green eyes?
Let's ask that question.
Can you look at the picture
and figure that out?
How many women had green eyes?
Okay, well, we would look
in this circle for G
and we've got 25 plus 12,
right, together?
So the answer
to that one would've been 37.
So a number
of questions could be asked,
I just happened
to ask how many women were
in the group.
I'm going to do another
problem on--
if you want it to look
at some more examples
on the next video.
In fact, on the next Venn
diagram, we're going
to do a problem
where we're going to have
to draw 3 sets.
So it gets a lot more
complicated
when you're not just talking
about 2 things
but 3 different things.
Please visit my website
at yourmathgal.com
where you can view all
of my videos
which are organized by topic.