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Learning Exercises for Section 27.3 1. Set up and complete a simulation of tossing a die 100 times. How do the probabilities of each outcome compare with the theoretical probabilities? Do the same simulation for 500 repetitions. What pattern do you notice as the number of repetitions increases? 2. a. Set up and complete a simulation to find the probability of getting green twice in a row if a spinner is on a circular region that is 1/3 green, 1/6 blue, 1/3 red, and the rest yellow. The spinner is spun twice. Carry out the simulation 30 times and record the outcomes. (Your record should include colors.) Answer parts (b) through (e) based on the outcomes of your experiment in part (a), and tell whether your experimental values are close to the theoretical values. b. Which outcome is most likely? Why? c. What is the probability of getting a green on the first spin and a blue on the second? d. What is the probability of getting a green on one of the spins and a blue on the other? Why is this question different from the question in part (c)? e. What is the probability of not getting green twice in a row? (Hint: There is an easy way to compute the probability.) 3. On one run of the free-throw simulation in Activity 10, the event YYYYN had a proportion 0.319. What does that mean? 4. Does a simulation using randomly generated numbers give theoretical or experimental probabilities? Explain. 5. a. Go to http://illuminations.nctm.org/ and click on "Interactives." In the search bar, type in "Adjustable Spinner." Scroll down to the "Adjustable Spinner" option. Set the sectors and the number of probabilities for the sectors by moving the dots on the circle or by moving the buttons for each color. Set the number of spins to 1000, and click on "Spin." You will see how the spinner works. You can click "Skip to end" to see the end results of all the spins. Write down the numbers in the results frame. These are the relative sizes of the regions of the circles and show theoretical probabilities (but in percents). b. Use this spinner activity to simulate a five-outcome experiment with unequally likely outcomes, and run the simulation 100 times. How do the experimental results compare with the theoretical ones in the table at the bottom of the screen? c. Repeat with a run of 1000 simulations. How do the experimental results compare with the theoretical ones? d. Repeat with a run of 10,000 simulations. How do the experimental results compare with the theoretical ones? Supplementary Learning Exercises for Section 27.3

Learning Exercises for Section 27.3
1. Set up and complete a simulation of tossing a die 100 times. How do the probabilities of each outcome compare with the theoretical probabilities? Do the same simulation for 500 repetitions. What pattern do you notice as the number of repetitions increases?
2. a. Set up and complete a simulation to find the probability of getting green twice in a row if a spinner is on a circular region that is 1/3 green, 1/6 blue, 1/3 red, and the rest yellow. The spinner is spun twice. Carry out the simulation 30 times and record the outcomes. (Your record should include colors.)
Answer parts (b) through (e) based on the outcomes of your experiment in part (a), and tell whether your experimental values are close to the theoretical values.
b. Which outcome is most likely? Why?
c. What is the probability of getting a green on the first spin and a blue on the second?
d. What is the probability of getting a green on one of the spins and a blue on the other? Why is this question different from the question in part (c)?
e. What is the probability of not getting green twice in a row? (Hint: There is an easy way to compute the probability.)
3. On one run of the free-throw simulation in Activity 10, the event YYYYN had a proportion 0.319. What does that mean?
4. Does a simulation using randomly generated numbers give theoretical or experimental probabilities? Explain.
5. a. Go to http://illuminations.nctm.org/ and click on "Interactives." In the search bar, type in "Adjustable Spinner." Scroll down to the "Adjustable Spinner" option. Set the sectors and the number of probabilities for the sectors by moving the dots on the circle or by moving the buttons for each color. Set the number of spins to 1000, and click on "Spin." You will see how the spinner works. You can click "Skip to end" to see the end results of all the spins. Write down the numbers in the results frame. These are the relative sizes of the regions of the circles and show theoretical probabilities (but in percents).
b. Use this spinner activity to simulate a five-outcome experiment with unequally likely outcomes, and run the simulation 100 times. How do the experimental results compare with the theoretical ones in the table at the bottom of the screen?
c. Repeat with a run of 1000 simulations. How do the experimental results compare with the theoretical ones?
d. Repeat with a run of 10,000 simulations. How do the experimental results compare with the theoretical ones?
Supplementary Learning Exercises for Section 27.3

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