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Chapter 7 Assignment These assignments will NOT be accepted unless typed. (Yes, the tables must be typed too. You are to make tables, not columns. If you need help with creating tables, just ask.) You will not be turning in a preliminary draft. You can still ask me questions to make sure you are doing it correctly. Type the experiment questions along with the results. You will be marked down without these. You will perform three probability experiments: 1) Rolling dice (one and two) 2) Selecting a number 1-10 from a bag (with replacement) and using randint function to generate a numbers 1-10 list (uses “with replacement”) 3) Another probability experiment of your choice involving the procedure of “without replacement” Chapter 7 Schedule Date Topic/Assignment Date Topic/Assignment 3/21-3/22 PPT: Chance & Probability 3/30 PPT: Permutations, Combinations, Fundamental Counting Principle GW: Shut the Box 3/23 PPT: Probability Models, Rules 4/2 GW: Jeopardy 4/3 Take any missing exams 4/4-4/5 Turn in Chapter 7 HW of Probability HW: Intro to Ch. 7 Probability Experiments Assignment 3/26 PPT: Addition Rule GW: White Book Activity 3/27 3/28-3/29 PPT: Multiplication Rule, Conditional Probability Take Chapter 7 Test GW: White Book Activity HW: Hand out ec assignment Numb3rs Episode 303 GW: Birthday Surprise (Complements) Report on the following results for experiment #1 1) What is the sample space for rolling 1 die? 2) What are the theoretical probabilities for the outcomes in rolling 1 die, in fraction form? Write a probability model for this. 3) Roll 1 die 36 times. Record your results. How does your empirical data compare with the theoretical probability for the outcomes? Record the probabilities (empirical and theoretical) for the sample space, side by side in a table in fraction form. 4) Are the outcomes for this experiment mutually exclusive and independent? Explain your answer. 5) What is the sample space for rolling 2 dice? (Use the sum of the dice) 6) What are the theoretical probabilities for the outcomes in rolling 2 dice, in fraction form? Write a probability model for this. 7) Roll 2 dice 36 times. Record your results (their sums). How does your empirical data compare with the theoretical probability for the outcomes? Record the probabilities (empirical and theoretical) for the sample space, side by side in a table in fraction form. 8) Are the outcomes for this experiment mutually exclusive and independent? Explain your answer. 9) If your empirical probabilities did not match the theoretical probabilities, how can you do the experiment differently so they could match, or come closer, the next time? 10) Using the empirical and theoretical data you have gathered for rolling 1 die and 2 dice, create the following: a. An event using the theoretical data for rolling 2 dice (i.e., rolling an odd number—use something different please!). i. Calculate the theoretical data and empirical data based on this new event. ii. Make comparisons regarding how close your data is now to how close it was originally. b. Using the same event as part a above for rolling 2 dice, repeat using theoretical data for rolling 1 die (i.e., rolling an odd number – again, please don’t use that one). i. Calculate the theoretical data and empirical data based on this event. ii. Make comparisons regarding how close your data is now to how it is to the data in part a. In some cases, it may be that part b was not possible because you chose something part a was able to do that part b wasn’t. Don’t change your events. Report on the following results for experiment #2 1) What is the sample space? 2) What are the theoretical probabilities for each outcome? Write out as a probability model. 3) Find the theoretical probability of choosing a 5 or an 8. 4) Choose 50 numbers using randint(1,10,50). List the numbers which were drawn, in order. 5) What was the empirical probability of choosing a 5 or an 8 in your probability experiment? 6) Find the theoretical probability of choosing a number less than 4 or an odd number. Write the formula for this. 7) Choose 50 numbers by choosing numbers from a bag (choose the number, record it, replace it, then repeat). 8) What was the empirical probability of choosing a number less than 4 or an odd number in your probability experiment? 9) Are the outcomes for either part of this experiment mutually exclusive and independent? Explain your answer. 10) Did changing the method of choosing numbers have an effect on the outcomes? Explain. Report on the following results for experiment #3 1) What is your probability experiment? 2) What is your sample space? 3) What are the theoretical probabilities for each outcome? 4) Conduct your probability experiment. Your experiment must include a procedure “without replacement”; that is if you choose a number from a bag, you don’t put it back. The probability of the next item chosen has changed (out of 10 has now changed to out of 9). You need to repeat the experiment a sufficient number of times as to get enough data as you did in experiments #1 and 2. 5) Report your data. What are the empirical probabilities for this data? Compare this data to the theoretical probabilities. Were they close? 6) If your experiment was “mutually exclusive”, how can you change it to “not mutually exclusive”; if it was “not mutually exclusive”, how can you change it to “mutually exclusive”?