The **Binomial Probability Function** can be used to calculate the
probability of **"x"** successes from **"n"** trials with the
probability of success on each trial **"p"**. We say **"x"**, the
random variable, is distributed Binomial**(n,p,x)**.

**Sample Problem**

Say we want to calculate the probability
of 3 successes from a total of 10 independent trials where the
probability of success on each trial is 0.35. Here : ** "n" = 10
,"x" = 3 , and "p"= 0.35 **.

On the calculator start from a clear screen. Press
(you will see this screen)

**Arrow down** to choice **"0: binompdf ( "** Press .

(you will see this screen.)

You must enter ** n , p , x** in **that order** inside the
parenthesis. So for our problem we will enter **10** **.35**
. Don't forget the commas or the
closed parenthesis!

Now press **.252219625** will be displayed.
This is the probability of 3 successes from 10 trials where the
probability of success on each trial is 0.35 .

What if you wanted to know the probability of 5 successes from this
same distribution?

You do not have to start over from the
beginning.

To calculate the probability of 5 successes from the
same problem you do not have to start over. Simply press

(this screen will reappear.)

Now you can **Arrow left** to highlight the ** 3** . Next
press . This will replace the 3 with
a 5. Press **.1535704107**
will be displayed. This is the probability of 5 successes from 10 trials
where the probability of success on each trial is 0.35.

**"Binomcdf("** will calculate the cumulative probability from 0
through X. [e.g. **Binomcdf (10 , .20 , 4)** will calculate the
probability of **x = 0+1+2+3+4 success**, where n=10, p=0.20, which
= **.9672065025 ]**

**Plot** a particular **Binomial Distribution.**

Let's use this last problem's data where **"n"= 10, "p"= 0.35.**
First press

**"EDIT"**
should be highlighted. Press

**Make sure all list are clear.** [ To clear L1 you **Arrow up**
to and highlight L1, press . Follow the same procedure to clear any
list.]

Enter the numbers **{1,2,3,4,5,6,7,8,9,10}** into **List
1.**

These are the **"x"** values. Next we want to enter a
**formula** into **List 2**.

First highlight **L2**. You should see this screen.

Now press ** 10**
**MATH**

Next **Arrow left** to "**PRB**"

highlight
"**3: nCr**"

Press
. (this screen will appear)

Next press **.35**
.

You will see this text scroll
across the bottom of the screen:

Now press **.65** **10**

You will be able to see all the
text by **Arrow left** or **right** .

Now press These probabilities will appear in
**List2**. (See below)

[The numbers in List2 are the probabilities associated with the "x"
values from List1.] (i.e. The probability that **x = 5** is
**0.15357, etc. )**

Now to see a plot we must go to the STAT PLOT so press **Y =**

(You will see this
screen.)

**"1:Plot1..."** should be highlighted. Press Make sure **On** is highlighted and
press . (you should be looking at
this screen.)

**Arrow down** and highlight the first option right of
**"Type"** (Scatter Plot)

And press Make sure ** Xlist: L1 , Ylist:
L2**

Now, as always, we need to adjust the window to fit our data or you may press to have the calculator automatically adjust the window.

Press **Xmin: 0 , Xmax: 11 ,
Xscl 1 , Ymin: 0 , Ymax: 0.5 , Yscl 0.1** .

Press . (this screen will appear)

Notice that even with only 10 data points this graph resembles a "bell curve."

You can read the probabilities directly off this screen by pressing
and **Arrow right** or
**Left**. (see screen)

Here "x" is the number of successes and "y" is the corresponding probability. So from this screen we see that there is a .2377 chance of 4 successes from 10 trials where the probability of success on each trial is 0.35.

[You can **Arrow left** or **right** to read each desired
probability.] Notice also that in the upper left screen P1: L1,L2 is
displayed. This tells us that we are using PLOT1 and the data from
LIST1, and LIST2.