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Dice and Probability Project

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Submitted By Shamara23
Words 716
Pages 3
Shamara
MAT 143
03/02/16
Module 6 Project

1. (5 pts) You are going to roll a pair of dice 108 times and record the sum of each roll. Before beginning, make a prediction about how you think the sums will be distributed. (Each sum will occur equally often, there will be more 12s than any other sum, there will be more 5s than any other sum, etc.) Record your prediction here:
I think in the beginning the sums will vary but then eventually repeat, and there will be more 7’s then any other sum.

2. (5 pts) Roll the dice 108 times and record the sum of each roll in the table provided below.

7 3 4 8 11 3 6 4 2 10 5 9
7 7 12 10 10 3 5 2 2 6 4 8
5 9 2 7 9 7 7 12 12 4 6 3
9 8 2 3 12 6 9 7 7 7 12 5
6 8 2 4 7 7 8 10 3 5 5 4
7 7 12 4 6 8 3 12 7 7 8 3 10 3 5 8 7 9 6 6 12 4 7 9
9 11 4 5 2 5 2 3 5 3 10 2
2 4 3 6 3 10 7 7 9 8 5 12

3. (22 pts) Find the experimental probability of rolling each sum. Fill out the following table:

Sum of the dice Number of times each sum occurred Probability of occurrence for each sum out of your 108 total rolls (record your probabilities to three decimal places)
2 10 .092
3 13 .120
4 10 .092
5 11 .101
6 9 .083
7 19 .175
8 9 .083
9 9 .083
10 7 .064
11 2 .018
12 9 .083

4. (5 pts) Compare your outcomes to your prediction. Was your prediction correct? Why do you think this happened?
Yes, my predictions were correct and I think it just happened coincidently.
5. (5 pts) What number(s) occurred most often? Least often? Why do you think that is?
7’s occurred the most, 11’s were the least and I think this occurred due to the variety of outcomes that were rolled to get the sums.
6. (38 pts) Now, construct a sample space of equally likely outcomes when rolling a pair of dice and use it to determine the theoretical probability of each sum occurring. Fill in the chart below with

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