Question

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:

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

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
3
4
5
6
7
8
9
10
11
12

4. (5 pts) Compare your outcomes to your prediction. Was your prediction correct? Why do you think this happened?

5. (5 pts) What number(s) occurred most often? Least often? Why do you think that is?

Answer 1

The problem is explained in two parts.

Part A : Understanding the chance of getting a particular sum on rolling two dice.

Theoretically, we find the probability of getting a particular sum. We do the following sum

This also the expected distribution of the sum when we roll the dice.

Part B : Rolling the dice 108 times

We see that is different in what is the expected number of sum or expected probability distribution and the actual probability distribution.

This is because of random sampling error. As the sample size increases, that is from 108 sample if increase it to 1000 samples, the observed probability will match with expected probability.