Die and Probability activity
by Johnnie Ostermeyer

I used this in my Geometry class with geometric probability. The day before the activity we did theoretical probability of dies, coins, and cards exedra. Then we talked about experimental probability We did a few short experimental things like roll a die 10 times and record the numbers and then flip a coin 20 times and record heads or tails.  The students had to tell me both the theoretical and the experimental probability of these experiments.
Then I showed them how to use the calculator to generate random numbers.  I paired them up for this activity and these would be their partners for tomorrow. Then the next day we did the Die and Probability activity. I only did one die not the dies for time purposes. 
|It went well the students like to use the graphing calculator when possible to do things other than the basic operations.  I changed this a little I made them show me their histogram before going on so that way they did not just make up numbers.  Then I had them do the same thing with a different amount of numbers generated then 100 they choose the number.  It went will and I think that students understood that theoretical probability never changes but experimental does.  Also, that the more an experiment is repeated the closer you will get the theoretical probability.

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Die and Probability

Objective: Using random numbers to simulate 100 tosses of a 6 sided die, determine the experimental probability of tossing a 1, 2, 3, etc.

1. Generate 100 random integers from 1 to 6.

            From the home screen, press the MATH key, arrow over to PRB and select             randint(. The command format is: randint( start, end, # of integers ).

Type: randint( 1,6,100) L 1. This command generates 100 integers form 1 to 6,             inclusive, and store them in a List ( L ).

2. Display the list.

From the home screen, press STAT and choose EDIT. The List will appear on the screen.  L 1 (1) = 6 indicates the first toss was 6, L 1 (2) = 3 indicates the second toss was 3.

3. Create a Histogram (Frequency vs. Integer tossed).

            The Histogram is created through the STATPLOT menu.

From STATPLOT, select Plot1 and turn Plot1 ON. (All other points should be OFF).  Select Histogram: Xlist: L 1 and Freq: 1.

4. Adjust the window to fit. [ 0, 10, 1, −5, 30, 5 ]

                                                Tosses    Frequency   

5. Display the histogram.

Press the Graph key. The Histogram will appear in the window. Trace across the histogram. The            cursor jumps to the top of each bar. Notice what appears at the bottom of the screen.

6. Show teacher your Histogram.                               Teachers Initials: ____________

7. List the frequency of each integer and calculate the experimental probability.

Number           Theoretical

                        probability

Frequency

100                          your #

Exp. Probability

100                             your #

1                             .17

11                           148

.11                              .16

2                             .17

21                           149

.21 
17

3                             .17

17                           151

.17                              .17

4                             .17

14                           154

.14                              .17

5                             .17

20                           155

.20                              .17

6                             .17

17                           143

.17                              .16

How do the experimental probabilities compare to the theoretical probabilities? ___they are close in most cases but not exact___

Are the bars equal in height? __No___ Should they be? _____No_____

How many numbers did you choose to generate? ___900____