In this Activity the Simulation feature in StatCrunch will be used to study probabilities when a pair of dice are rolled. Consider rolling a pair of 3-sided dice many times and adding up the 2 dice each time. If the sides on the dice are 1, 2, and 3, the possible totals for your addition are 2, 3, 4, 5, and 6. Specifically these are the results.....

Total of 2 = 1 + 1 (1 result)

Total of 3 = 1 + 2 = 2 + 1 (2 results)

Total of 4 = 1 + 3 = 2 + 2 = 3 + 1 (3 results)

Total of 5 = 2 + 3 = 3 + 2 (2 results)

Total of 6 = 3 + 3 ( 1 result)

So, there are 9 (3 x 3) possible results for the 5 totals.

The Simulation feature in StatCrunch will allow you to perform this task 1000 times, and it will record your results.

PART A OF YOUR WORK: Run this simulation 1000 times. Save the output, and indicate the results for each of the 5 totals. StatCrunch provides a bar graph with the heights of the bars indicating the frequencies of each of the 5 totals, include that bar graph with your results. Your answers should be close to the following.....

Total of 2: should be close to 111 because 1000 x (1/9) = 111.11

Total of 3: should be close to 222 because 1000 x (2/9) = 222.22

Total of 4: should be close to 333 because 1000 x (3/9) = 333.33

Total of 5: should be close to 222 because 1000 x (2/9) = 222.22

Total of 6: should be close to 111 because 1000 x (1/9) = 111.11

PART B OF YOUR WORK: Most dice have 6 sides, and the total when adding up a pair of dice are the values 2 to 12. Determine the number of results which are possible for each of the values from 2 to 12, like what was done above for 3-sided dice (1-2-3-2-1). HINT: 3 x 3 = 9 total results for a pair of 3-sided dice. It will be 6 x 6 = 36 total results for a pair of 6-sided dice.

PART C OF YOUR WORK: Run this simulation 1000 times. Save the output, and indicate the results for each of the 11 (2 through 12) totals. StatCrunch provides a bar graph with the heights of the bars indicating the frequencies of each of the 11 totals, include that bar graph with your results.