Module 3 – Experimental vs. Theoretical Probability

Definitions:

v     Experimental Probability- The process of determining the probability of an event by carrying out an experiment where trials are conducted and data is recorded to determine the probability of an event.

v     Theoretical Probability – The process of finding the probability of an event mathematically utilizing charts, tables, listings, and formulas.

 

As you might recall we defined probability in Module 1:

The probability of an event is a ratio that compares the number of favorable outcomes to the number of possible outcomes.

The probability of an event occurring must fall between 0% and 100% inclusive.  It is impossible for an  event to happen less than 0 or greater than 100%.  If we change the percentages into numbers, all probability events occur between 0 and 1 inclusive.  In this module we will compare and discuss both experimental and theoretical probability.

Example #1 – Drawing items from a bag:  A probability event is set up so that 12 colored blocks of equal size and shape are placed in a bag.  There are 4 blue, 5 green, and 3 red blocks.  If a block was removed from the bag what is the probability that a green block was removed.  According to the formula above,

This represents the theoretical probability of drawing out a green block.  On the other hand we could actually set up the experiment and begin trials to determine the number of times a green block is pulled.  These trials would represent the experimental probability.  If we were to perform the experiment 12 times we may or may not see the green block 5 times in those 12 trials.  Although, theory dictates that as long as the trials are independent and fair, the more trials that are performed the closer the experimental probability will match the theoretical probability.


 

 

Module 3 Assignment:

1.      Conduct an experiment using three coins.  In this experiment you will be flipping three coins 100 times and recording the results of each toss.  When you have finished flipping the coins 100 times, record your results in a table to share with the rest of the class.

2.      Go to the following coin flip generator website and repeat the experiment (http://www.random.org/coins/).  Flip the set of three coins 100 times and record your results.  Present your data in a table to share with the rest of the class.  Prepare a comparison of the two experiments.  Did you notice any differences?  Is there anything in the experiments that might have affected the outcomes enough that made these two experiments different?

3.      Calculate the theoretical probability of flipping three coins.  Compare the theoretical calculation with the experimental results.  How does the experimental data compare with the theoretical calculation?  Be ready to discuss with the class.

4.      Conduct an experiment with two number cubes (dice).  In this experiment, roll the number cubes 100 times and record the sum of the two numbers.  Record your results on the spreadsheet file that is included here and save the file. (Table Data Spreadsheet).

5.      Go to the following dice roll generator website and repeat the experiment (http://www.random.org/dice/).  Roll the dice 100 times and record you results.  Again record your results on the spreadsheet file that you have.  Do you notice any differences between the actual rolling of the dice and the random generator on the internet?  Is there anything in the experiments that might have affected the outcomes enough that made these two experiments different?

6.      Calculate the theoretical probability of rolling the two number cubes.  Compare the theoretical calculation with the experimental results.  How does the experimental data compare with the theoretical calculation?  Be ready to discuss with the class.

7.      Write a response to the following question: 

When the number of experimental events increases, how does the experimental probability compare to the theoretical probability?  Explain your reasoning.

 

 

Grading Rubric For Module 3

Problem (A) Exceeds Standard (B) Meets Standard (C) Approaches Standard (D) Emerging
1 100 experiment samples conducted and outcomes neatly organized and presented to the class. 100 experiment samples conducted and outcomes unorganized when presented to the class. 100 experiment samples conducted and data not available to present to the class. Less than 100 experiment samples conducted and data not available to present to the class.
2 100 experiment samples conducted on random coin flip generator and outcomes neatly organized and presented to the class. Comparison presented and two questions answered and justified. 100 experiment samples conducted on random coin flip generator and outcomes neatly organized and presented to the class. Comparison not presented and two questions answered and justified with few errors. 100 experiment samples conducted on random coin flip generator and outcomes not organized when presented to the class. Comparison not presented and two questions unanswered and unjustified with significant errors. Less than 100 experiment samples conducted on random coin flip generator and outcomes not organized when presented to the class. Comparison not presented and two questions unanswered and unjustified with significant errors.
3 Response correct for theoretical probability.  Comparison between theoretical and experimental probability presented and justified correctly. Response correct for theoretical probability.  Comparison between theoretical and experimental probability presented and justified with few errors. Response correct for theoretical probability.  Comparison between theoretical and experimental missing and\or contains significant errors. Response incorrect for theoretical probability.  Comparison between theoretical and experimental missing and\or contains significant errors.
4 100 experiment samples conducted and outcomes neatly organized on spreadsheet and presented to the class. 100 experiment samples conducted and outcomes on spreadsheet unorganized when presented to the class. 100 experiment samples conducted and data not available on spreadsheet to present to the class. Less than 100 experiment samples conducted and data not entered on the spreadsheet.
5 100 experiment samples conducted on random dice roll generator and outcomes neatly organized on spreadsheet and presented to the class. Comparison presented and two questions answered and justified. 100 experiment samples conducted on random dice roll generator and outcomes neatly organized on spreadsheet and presented to the class. Comparison not presented and two questions answered and justified with few errors. 100 experiment samples conducted on random dice roll generator and outcomes not organized on spreadsheet when presented to the class. Comparison not presented and two questions unanswered and unjustified with significant errors. Less than 100 experiment samples conducted on random dice roll generator and outcomes not organized on spreadsheet when presented to the class. Comparison not presented and two questions unanswered and unjustified with significant errors.
6 Response correct for theoretical probability.  Comparison between theoretical and experimental probability presented and justified correctly. Response correct for theoretical probability.  Comparison between theoretical and experimental probability presented and justified with few errors. Response correct for theoretical probability.  Comparison between theoretical and experimental missing and\or contains significant errors. Response incorrect for theoretical probability.  Comparison between theoretical and experimental missing and\or contains significant errors.
7 Correct answer and supporting information included. Correct answer and supporting information included, few errors. Correct answer and supporting information not included, significant errors. Incorrect answer and supporting information not included, significant errors.