This program finds either the binomial probability of a single event, or 

the sum of probabilites of a few events, or plots the probability 

distribution for all possible events.

For the TI-82:

----begin documentation----

A binomial situation is defined to have exactly two possible outcomes.  

For example, a voter may vote either for a given measure or against it.  

Let the probability of success on a single event be known and given by  P  

for some 0<P<1.

 

Now we can sample  N  independent events and find the probabilities for  

R  successes.  For example, if a reliable poll says that  P=40%=0.40  of the 

voters will vote for Proposition A, and we randomly sample  N=8  voters, 

then we can find the probability that "exactly"  R=5  sampled voters will 

vote for Proposition A.  We will denote this  P(5 of 8), or simply P(5) for a

 "single" probability.

 

We may also want to find the probability of "at least"  5  voters of the  

N=8  sampled.  Now  R  varies from 5 to 6 to 7 to 8.  We may add these 

individual probabilities to find the  "sum".   When using the program, use the 

left- and right-arrow keys to scroll through the list of  P(R)s  after finding 

a "sum".

 

Finally, we may examine the probability "distribution" with  R  on the 

x-axis and  P(R)  on the y-axis.  This is especially instructive if  P 

 changes, say from 0.40  to  0.10.  Also as  N  increases,  the  distribution 

resembles a smooth bell-shaped curve.

 

Since students learning this distribution are not always aware of the 

restrictions on  P,  N  &  R,  then special error messages are included in this 

program.

 

Any questionsor comments can be directed to:

 

Mark Harbison

San Diego Mesa College

San Diego, CA  92111-4998

 

----end documentation----