Download “Dice Sums” Activity Standards Addressed

“Dice Sums” Activity
Standards Addressed:
Wisconsin Common Core Standards Addressed:
Statistics and Probability
Investigate chance processes and develop, use, and evaluate probability models.
Learning Objectives:
Students will be able to predict the probability of an event by performing that event.
Students will be able to create a model to find the probability of an event.
Problem:
Roll two dice at once and if the sum is 2, 3, 4, 5, 10, 11, or 12, you win. If the sum is 6, 7, 8, or 9,
then I win. Is this game fair? (Decide what it means that a game of chance is “fair.”)
Do this problem in two ways:
1. Actually play the game multiple times and collect data to decide.
2. Do a theoretical analysis of the problem to decide.
Instruction:
1. Students will each be given two six-sided di.
2. They will be asked to record the data they find.
3. After each student has had the chance to play for some time, we will record the data on
the board. (Recording how many times they won compared to me)
4. Students will make a conclusion on whether or not they think the game is fair based on
the classroom data.
5. Students will then be asked to come up with a theoretical analysis to decide whether or
not the game is fair. This needs to include a why and mathematical proof to prove their
conclusion.
6. Students will share their ideas with the rest of the class.
Solution:
An example of a student’s work to prove whether or not the game is fair…
Students may provide a sample space for a roll of two dice:
The student would use this sample space to notice that there are 36 equally likely outcomes, so
the probability of each outcome is 1/36. The student could use this sample space to compute
the probability of the event obtaining the sum of a number 2-12 by counting the number of
possible outcomes that have the sum of that number.
Example: “obtaining the sum of 3” (1,2) and (2,1) so the P(Sum=3) can be written as
1/36 + 1/36 = 2/36 or 1/18
The student would continue this process to find the probability for all numbers 2-12; to decide
if the student or the teacher has a better probability of winning the game (is the game fair or
not?)
Student’s numbers:
2: 1/36
3: 2/36
4: 3/36
5: 4/36
10: 3/36
11: 2/36
12: 1/36
Total chance of winning: 16/36
Teacher’s numbers:
6: 5/36
7: 6/36
8: 5/36
9: 4/36
Total chance of winning: 20/36
From this the student will be able to see that the game is unfair and that the teacher has a
better chance of winning based off of probability.
Homework:
How could you change the rules of the “Dice Sums” activity to make the game fair?