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How to pronounce 244 in English?

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- Now that we're comfortable working
with basic probabilities, we're going
to look at different ways we can organize our probabilities
and information.
In today's video, we're going to look at the question,
how do we organize probability information in a table?
Specifically, we're going to be in the context of what
is called a contingency table, which is basically
just a table that lists results in relation to two variables.
These tables and this information
will make calculating probabilities easier.
And what makes it easier is quite often
we will add a column and row for totals.
So for example, let's say we've done a survey.
And we're comparing whether or not
people have speeding tickets in the last year
or no speeding tickets in the last year.
And we're going to break this up into three groups.
The first group are going to be our younger
drivers, the under-21 drivers.
And then we're going to also look at the 21
to 25-year-old drivers.
And then we'll also look at the over 25 drivers.
And the survey is conducted.
And there's 82 under-20 ones with the ticket,
17 without a ticket in the past year.
For the 21 to 25's there were 39 with a speeding ticket and 27
without.
And for the over 25, there's 18 with a speeding ticket and 61
without.
Now with this contingency table, it's
going to be helpful that we're going
to add an extra row and an extra column
if it's not there already.
That's going to give us the totals.
And these totals are going to make
calculating individual probability questions much more
efficient.
So if we total that under-21, we see we have 99 surveyed.
The 21 to 25--
total that, we get 66 surveyed.
Total the over 25, we get 79 surveyed.
Working across the rows 82 plus 39 plus 18,
there's 139 people surveyed who got a speeding
ticket in the last year.
The no tickets 17 plus 27 plus 61 is 105.
And for the totals 99 plus 66 plus 79
gives us 244 people total in the survey.
And a good way to check that that totals correct
is if we add the other combination, 139 plus 105.
That should also equal the 244, which it does.
And so what we have there as that example
is a contingency table.
Now we're ready to find some probabilities
off this contingency table.
For example, if I were to know the probability that someone
is 21 to 25, I can see very quickly on my contingency table
that there are 66 people in the 21 to 25
range out of a total of 244 people.
And so when I divide 66 by 244, we
can quickly get our probability 0.2705.
We could also do maybe the probability
that someone has no tickets.
Very similar, I'd say, well, no tickets
the total there is 105 out of the grand total, which is 244.
And then we divide 105 by 244, we
get 0.4305 for our probability.
We can also do ands and we can do or's We
can find-- let's combine these together-- the probability
that someone is 21 through 25 and has no tickets.
Well, the 21 to 25 and have no tickets are when both of those
occur together at the same time.
That's where they overlap.
Here in the middle, we have 27 people who are no tickets,
and they're 21 to 25 out of the total of the whole group
is still 244.
And so when I divide 27 by 244 we get 0.1107.
And we can change that to an or.
We can find the probability that someone's 21 to 25
or has no tickets.
And if you remember the or formula says
we have to add the individual pieces
and then subtract where they overlap.
So 21 to 25, there's 66 of them plus the no tickets,
there's 105 of them.
But we have to subtract where they overlap,
because these 27 where they overlap
have been counted twice in both the column and the row.
So let me subtract off the 27 out of the 244.
When we do that math on our calculator,
we get 0.5902 about a 59% probability
they're one of those two.
We can even do given probabilities.
Let's do the probability that we're in that 21 to 25 range--
let's get rid of the circles we don't need--
given we know the person has no tickets.
Well, with a given probability, we are looking for both of them
or the overlap divided by the given information.
So where they overlap 21 to 25 and no tickets,
they overlap with 27.
But we're going to divide by the given information.
This time it's not the 244, because we've
shrunk our sample size.
Now we're just interested in those that have no tickets.
We're only interested in that 105.
And so with the given information
shrinking the sample size, now the probability is 0.2571.
We can switch that and see how that probability compares.
The probability they have no tickets, given they're
between 21 and 25 years old.
You might pause the video and see
if you can figure this one out on your own.
With a given probability, we need
to find where they overlap divided by the probability
of the given information.
They overlap, again, no tickets in 21 to 25
with these 27 individuals.
However now our sample space, the given information,
is just 21 to 25 years old.
And that's the 66.
So we'll do 27 divided by the 66 to get
our probability of 0.4091.
And you can see how we move through each
of these probabilities at a much greater accelerated pace
when we have the contingency table
to organize our data for us.
That's the nice thing about the contingency table.
One more thing I want to look at,
though, is we have this vocabulary word
from our previous video of independence.
So what I want m are being 21 to 25
and having no tickets independent?
Does that mean being 21 to 25 has no impact on
whether or not you had a ticket in the past year?
Well, we talked about there being
three different formulas we could
use in order to show this.
One of those three formulas says that a given probability
should not change the probability if they
are in fact independent.
In other words, the probability of they're being 21 to 25
and given they have no tickets should
be the same as the probability of just being 21 to 25
if they're independent, because the tickets shouldn't
impact that at all.
Well, we just found both of these pieces.
The probability of being 21 to 25 given we have no tickets
is actually here in number 5, that was 0.2571
And the probability of being 21 to 25
we found in part one, that's 0.2705.
And we see that these guys are different.
Therefore, the probability is changed
once we have given information and shrunk down
the sample size.
That means these two variables are actually
dependent on each other.
So all we're looking at today is organizing in our probability
information in a contingency table
and taking a look at how that helps
facilitate calculating the actual individual
probabilities.
It also gives us an opportunity to practice more with and
or and the given probabilities.
So take a look at these on the homework assignment,
come to class ready to discuss them,
and work with these contingency tables a little bit more.

- Now that we're comfortable working

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How to pronounce 244 in English?

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