This is a video on plotting the
complement of an interval
on a number line.
The question states:
You want to find the probability
that at least 4 people
in your class have a last name
that contains the letter "W".
You will need to first find the complement
of "at least 4".
Sketch this complement
on the number line.
Let's start out thinking about what
it means to say at least 4.
The way I do that
is I first just write down
a bunch of numbers nearby 4.
I write down:  0, 1, 2, 3
4, 5, 6, 7, and 8.
I want to think about, what does it mean to say
"at least 4"?
Let's think about the words "at least".
What I do know is that you
must be at least 21 years old to enter a bar.
And that means that you can be 21.
You can also be 22 or 23 or 24.  All the way up.
You can't be, say, 20 or 19.
So "at least 4"
also needs to make sure that you are
4 or larger.  4 is ok, just
like 21 is ok to be at least 21.
Then 5, 6, 7, and 8 are ok.
Notice that if we are talking about at least
people, it doesn't make any sense
to go into fractions or
decimals, like 5.7.  You can't have
5.7 people having a name
that has the letter "W" in it.
In particular, I will circle "at least 4 people".
Those are the numbers from 4 to 8.
4, 5, 6,
7 and 8.
Next, I want to find the complement
of these numbers.  The complement
of a group of numbers,
all the numbers that are not circled.
In particular,
there is 0,
1, 2,
and 3.
Now I just have to sketch these on a number line.
I do so.  I draw a number line.
I plot the points at 0, 1,
2,
and 3.
There's my number line that shows
the complement
of "at least 4 people".
I am done with the problem.
Thank you for watching this video.
