#4105. Dice Activity - theoretical vs. experimental

Mathematics, level: Senior
Posted Thu Jan 31 13:46:14 PST 2008 by Tessa Townsend (townsetm@pickens.k12.sc.us).
Pickens High, Pickens,SC,USA
Materials Required: two dice for each group
Activity Time: 45-60 minutes
Concepts Taught: theoretical vs. experimental probability,sample sets, computing prob law of large numbers (optional)

I.) Students will work with one die first.
a. List the sample set for rolling one die.
b. Roll the die 20 times, recording the results.
c. Experimental Probability -- From the experiment, what was the probability of rolling a 1? Rolling a 2? . . . Rolling a 6? (Student answers will vary as the data varies.)
d. Theoretical probability -- have students compute the theoretical probability of rolling a 1, rolling a 2, . . . rolling a 6.
e. Compare results of theoretical vs. experimental probabilities.
II.) Students will work with two dice.
a. List the sample set for rolling two dice. (Students will take the sum of the dice.)
b. Roll the dice 20 times, recording the results.
c. Experimental Probability -- From the experiment, what was the probability of rolling a sum of 2? Rolling a sum of 3? . . . Rolling a sum of 12? (Student answers will vary as the data varies.)
d. Theoretical probability -- have students compute the theoretical probability of rolling a sum of 2, a sum of 3, . . . a sum of 12. Have students draw a histogram of the theoretical and discuss how it is normally distributed.
e. Compare the results of theoretical vs. experimental probabilities.

ADDITIONAL ACTIVITIES
I.) Using one die.
a. Have students do the above for one die. Students should have compared the experimental probability and theoretical and saw that they are not necessarily the same.
b. Have students roll the die an additional 20 times, recording results.
c. Have students find the experimental probabilities of all rolls (there are now 40 rolls of the die) and compare to the theoretical probability.
d. Have students roll the die again an additional 2o times, recording results.
e. Have students find the experimental probabilities of all rolls (there are now 60 rolls of the die) and compare to the theoretical probability.
f. Students should see that the experimental probabilities are converging to the theoretical probabilities. This illustrates the Law of Large Numbers. (This could also be done on a simulator such as the TI-83/84 Probability Pack Application or on a Java simulator found on the internet.)