complete the following:

Problem: To compare experimental and theoretical probability using 8-sided dice. Materials Needed: 2 Eight-Sided Dice (You may use the graphing calculator but you must record each outcome, so you may only roll once at time) Task: 1. Roll the dice 128 times. Make a tally chart of the outcomes in the table below Sum Tally Frequency Tick Marks) Experimental Total Number) Probability 3 4 5 6 7 8 10 11 12 13 14 15 16 NOTE: Your frequency should total 128, the number of times you rolled the dice. Check to make sure. 1. Use a distribution frequency to graph your results (Frequency vs. Sum). Answer the following questions: a. Which number never came up? Why? b. Which number has occurred the most frequently? Why do you think that happened? c. Describe any trends in the graph 2. Find the expected frequency if the die is rolled 104 times. To find the expected frequency, multiply the theoretical probability by 128 (the number of times the die would be tossed)Number Theoretical Probability Expected Frequency 1 N 4 10 11 12 13 14 15 16 1. Use a distribution frequency to graph your results (Expected Frequency vs. Sum). Answer the following questions: a. Which number would never came up? Why? b. Which number would you expect to occur the most frequently? c. Describe any trends in the graph. 2. Compare and contrast the experimental probability and the theoretical probability. a. Are there any probabilities the same? Any different? b. Would you expect them to be the same? c. How many rolled would be needed in order to have the theoretical and experimental probabilities close to being similar? 3. Compare the graphs. How are they similar? How are they different? 4. What conclusions can you draw from this experiment? 5. How would the probabilities change if two 12-sided die were used? What number would you expect to occur the most often? Explain. 6. What if a six-sided and a 12-sided die were used? Which number would you expect to come up the most often? Explain