WEBVTT

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- [Instructor] What we're
going to do in this video

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is learn how to use a graphing calculator,

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in particular a TI84.

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If you're using any other TI
Texas Instrument calculator

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it'll be very similar in
order to answer some questions

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dealing with geometric random variables.

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So, here we have a scenario.

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I keep picking cards from a standard deck

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until I get a king.

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So this is a class geometric
random variable here

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and it's important that
in this parentheses

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it says I replace the cards
if they are not a king

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and this important as we
talk about on other videos

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because the probability of
success each time can't change.

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And so we could define
some random variable X

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this is a geometric random
variable as being equal to

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the number of picks until we get a king.

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When we replace the cards
if they are not a king.

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And for this geometric random variable,

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what's the probability
of success on each trial?

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Remember what are the
conditions for a geometric

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random variable is that
probability of success

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does not change on each trial.

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Well the probability of
success is going to be equal to

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there's four kings in a
standard deck of 52, this is

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the same thing as one over 13.

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So this first question is
what is the probability that

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I need to pick five cards?

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Well this would be the
probability that our geometric

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random variable X is equal to
five and you could actually

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figure this out by hand,
but the whole point here

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is to think about how to
use a calculator and there's

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a function called geometpdf
which stands for geometric

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probability distribution
function, where what you have

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to pass it is the probability
of success on any given

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trial, one out of 13, and
then the particular value

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of that random variable
that you want to figure out

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the probability for, so
five right over there.

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Now just to be clear, if
you're doing this on an AP exam

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and this is one of the reasons
why a calculator is useful,

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you can use this on an AP
exam, AP statistics exam.

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It's important to tell the
graders if you're doing it

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on the free response that
this right over here is your

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P and that this right over
here is your five just so

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it's very clear that where you
actually got this information

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from or why you're actually typing it in.

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But let's just see how it
works, what this probability

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is actually going to amount to.

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Alright so I have my calculator
now and I just need to type

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in geometpdf and then those parameters.

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And so the place where I
find that function I press

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2nd, distribution right over
here, it's a little above

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the vars button.

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And then I click up, I can
scroll down or I could just

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go to the bottom of the list
and you can see the second

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from the bottom is
geometpdf, click Enter there.

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My P value, my probability
of success on each trial

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is one out of 13, and I want
to figure out the probability

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that I have to pick five cards.

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And so then click Enter,
click Enter again,

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and there you have it, it's about 0.056.

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So this is approximately 0.056.

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Now let's answer another
question, so here they say

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what is the probability that
I need to pick less than

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10 cards?

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So this is the probability
that X is less than 10

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or I could say this is equal
to the probability that

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X is less than or equal to nine.

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And I could say well this
is the probability that X

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is equal to one plus the
probability that X is equal to

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two all the way to the probability
that X is equal to nine.

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But that would take a
while, even if I used this

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function right over here.

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But lucky for us, there's
a cumulative distribution

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function, take some space
from the next question,

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this is going to be equal
to geometcdf, cumulative

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distribution function and once
again I pass the probability

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of success on any trial and
then up to including nine.

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So let's get the calculator out again.

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So we go to 2nd, distribution,
I click up and there we

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have it geomet cumulative
distribution function, press

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Enter, one out of 13 chance
of success on any trial.

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Up to and including nine, and then Enter.

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And there you have it, it's
approximately 51.3% or 0.513.

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So this is approximately 0.513.

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Now let's do one more.

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What is the probability that
I need to pick more than

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12 cards?

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And like I'll pause the video
and see if you can figure

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this one out, what function
would I use on my calculator,

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how would I set it up?

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Well the probability, this
is the probability that X

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is going to be greater than
12, which is equal to one

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minus the probably that x
is less than or equal to 12.

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And now this we could just use
the cumulative distribution

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function again, so this
is one minus geometcdf

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cumulative distribution
function, cdf, of one over 13

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and up to and including 12.

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So what is this going to be equal to?

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So 2nd, distribution, I click
up, I get to the function.

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Click Enter, and so I
already have that first,

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the probability of success on
every trial is one over 13,

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and then cumulative up to
12 and so I click Enter.

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And then well I could click
Enter there, but I really want

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to get one minus this
value, so I can do one minus

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2nd Answer, which would be
just one minus that value,

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which will be equal to there
you have it, it's about 38.3%

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or 0.383.

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So this is approximately
equal to 0.383 and we're done.