Simulations are used to relate probabilities by modeling complex situations as simple experiments. The document discusses using simulations on calculators and smartphones to model probabilities. It provides an example of simulating a baseball player's batting average over 10 at-bats. The simulation is run 25 times to determine the probability of getting exactly 3 hits is 8/25. The document also discusses using coins, cards, dice, and spinners to simulate different probability ratios like 1:2, 1:4, and 1:6. It concludes with assigning problem set questions from the textbook.

1. Section 4-2
Problem Solving Skills: Simulations

2. Essential Question
How are simulations used to relate probabilities?
Where you’ll see this:
Music, market research, games, statistics, probability

3. Vocabulary
1. Act It Out:
2. Simulation:

4. Vocabulary
1. Act It Out: Going through all of the motions of an experiment
2. Simulation:

5. Vocabulary
1. Act It Out: Going through all of the motions of an experiment
2. Simulation: A model of a situation where trials are carried
out, using a simple experiment to represent something
more complex

6. Vocabulary
1. Act It Out: Going through all of the motions of an experiment
2. Simulation: A model of a situation where trials are carried
out, using a simple experiment to represent something
more complex; This could be done by using a coin flip,
spinner, dice, cards, etc.

7. ProbSim on the TI-83/84

8. ProbSim on the TI-83/84
APPS

9. ProbSim on the TI-83/84
APPS Intro

10. ProbSim on the TI-83/84
APPS Intro Choices

11. ProbSim on the TI-83/84
APPS Intro Choices
Take some time to explore this app. You might also find apps for
your smartphone or iPod. Check the class wiki for some links,
or search your phone’s app store.

12. Example 1
Matt Mitarnowski has a batting average of .250. Design and run
a simulation for his next ten at bats. Record your results. What is
the probability that Matt gets exactly 3 hits?

13. Example 1
Matt Mitarnowski has a batting average of .250. Design and run
a simulation for his next ten at bats. Record your results. What is
the probability that Matt gets exactly 3 hits?
Sample simulation: Use a spinner with 4 sections. Spinning a 1
is a hit, while 2, 3, and 4 are all not hits. Spin the spinner 10
times and record the outcomes.

14. Example 1
Matt Mitarnowski has a batting average of .250. Design and run
a simulation for his next ten at bats. Record your results. What is
the probability that Matt gets exactly 3 hits?
Sample simulation: Use a spinner with 4 sections. Spinning a 1
is a hit, while 2, 3, and 4 are all not hits. Spin the spinner 10
times and record the outcomes.
You need to run the situation multiple times to get the probability.

15. Example 1
Matt Mitarnowski has a batting average of .250. Design and run
a simulation for his next ten at bats. Record your results. What is
the probability that Matt gets exactly 3 hits?
Sample simulation: Use a spinner with 4 sections. Spinning a 1
is a hit, while 2, 3, and 4 are all not hits. Spin the spinner 10
times and record the outcomes.
You need to run the situation multiple times to get the probability.
Run your simulation 25 times. Results will vary.

16. Example 1
My sample outcomes: 11: 3, 1, 2, 4, 1, 3, 2, 3, 4, 4
23: 4, 1, 3, 1, 2,
1: 4, 2, 1, 4, 4, 1, 1, 3, 4, 3 12: 3, 1, 1, 4, 2, 3, 2, 4, 2, 1 1, 4, 3, 2, 2
2: 2, 4, 1, 2, 1, 1, 4, 2, 3, 3 13: 2, 1, 2, 1, 4, 2, 3, 2, 1, 1
24: 4, 1, 3, 1, 2,
3: 1, 1, 3, 3, 4, 2, 1, 2, 4, 3 14: 4, 1, 4, 2, 2, 3, 1, 3, 2, 3 3, 4, 3, 1, 2
4: 3, 4, 3, 4, 3, 2, 1, 3, 4, 1 15: 2, 3, 3, 1, 1, 4, 2, 3, 2, 1
25: 2, 1, 4, 4, 3,
5: 2, 2, 4, 4, 2, 2, 1, 3, 3, 4 16: 2, 1, 1, 1, 3, 1 ,1, 2, 1, 4
3, 3, 2, 3, 3
6: 4, 4, 3, 2, 2, 4, 4, 2, 3, 2 17: 3, 4, 2, 4, 3, 1, 4, 2, 1, 4
7: 2, 1, 2, 3, 1, 3, 1, 3, 2, 1 18: 1, 4, 1, 1, 3, 1, 4, 4, 3, 4
8: 4, 2, 3, 1, 1, 3, 1, 3, 4, 4 19: 3, 4, 3, 3, 4, 3, 4, 4, 4, 1
9: 2, 2, 3, 2, 4, 3, 1, 2, 2, 1 20: 2, 3, 2, 2, 4, 3, 4, 1, 4, 1
10: 1, 4, 2, 2, 3, 4, 3, 1, 2, 3 21: 4, 1, 1, 3, 2, 2, 1, 3, 1, 2

17. Example 1
My sample outcomes: 11: 3, 1, 2, 4, 1, 3, 2, 3, 4, 4
23: 4, 1, 3, 1, 2,
1: 4, 2, 1, 4, 4, 1, 1, 3, 4, 3 12: 3, 1, 1, 4, 2, 3, 2, 4, 2, 1 1, 4, 3, 2, 2
2: 2, 4, 1, 2, 1, 1, 4, 2, 3, 3 13: 2, 1, 2, 1, 4, 2, 3, 2, 1, 1
24: 4, 1, 3, 1, 2,
3: 1, 1, 3, 3, 4, 2, 1, 2, 4, 3 14: 4, 1, 4, 2, 2, 3, 1, 3, 2, 3 3, 4, 3, 1, 2
4: 3, 4, 3, 4, 3, 2, 1, 3, 4, 1 15: 2, 3, 3, 1, 1, 4, 2, 3, 2, 1
25: 2, 1, 4, 4, 3,
5: 2, 2, 4, 4, 2, 2, 1, 3, 3, 4 16: 2, 1, 1, 1, 3, 1 ,1, 2, 1, 4
3, 3, 2, 3, 3
6: 4, 4, 3, 2, 2, 4, 4, 2, 3, 2 17: 3, 4, 2, 4, 3, 1, 4, 2, 1, 4
7: 2, 1, 2, 3, 1, 3, 1, 3, 2, 1 18: 1, 4, 1, 1, 3, 1, 4, 4, 3, 4
8: 4, 2, 3, 1, 1, 3, 1, 3, 4, 4 19: 3, 4, 3, 3, 4, 3, 4, 4, 4, 1
9: 2, 2, 3, 2, 4, 3, 1, 2, 2, 1 20: 2, 3, 2, 2, 4, 3, 4, 1, 4, 1
10: 1, 4, 2, 2, 3, 4, 3, 1, 2, 3 21: 4, 1, 1, 3, 2, 2, 1, 3, 1, 2

18. Example 1
My sample outcomes: 11: 3, 1, 2, 4, 1, 3, 2, 3, 4, 4
23: 4, 1, 3, 1, 2,
1: 4, 2, 1, 4, 4, 1, 1, 3, 4, 3 12: 3, 1, 1, 4, 2, 3, 2, 4, 2, 1 1, 4, 3, 2, 2
2: 2, 4, 1, 2, 1, 1, 4, 2, 3, 3 13: 2, 1, 2, 1, 4, 2, 3, 2, 1, 1
24: 4, 1, 3, 1, 2,
3: 1, 1, 3, 3, 4, 2, 1, 2, 4, 3 14: 4, 1, 4, 2, 2, 3, 1, 3, 2, 3 3, 4, 3, 1, 2
4: 3, 4, 3, 4, 3, 2, 1, 3, 4, 1 15: 2, 3, 3, 1, 1, 4, 2, 3, 2, 1
25: 2, 1, 4, 4, 3,
5: 2, 2, 4, 4, 2, 2, 1, 3, 3, 4 16: 2, 1, 1, 1, 3, 1 ,1, 2, 1, 4
3, 3, 2, 3, 3
6: 4, 4, 3, 2, 2, 4, 4, 2, 3, 2 17: 3, 4, 2, 4, 3, 1, 4, 2, 1, 4
7: 2, 1, 2, 3, 1, 3, 1, 3, 2, 1 18: 1, 4, 1, 1, 3, 1, 4, 4, 3, 4 Matt has an
8: 4, 2, 3, 1, 1, 3, 1, 3, 4, 4 19: 3, 4, 3, 3, 4, 3, 4, 4, 4, 1 8
chance
25
9: 2, 2, 3, 2, 4, 3, 1, 2, 2, 1 20: 2, 3, 2, 2, 4, 3, 4, 1, 4, 1
for 3 hits
10: 1, 4, 2, 2, 3, 4, 3, 1, 2, 3 21: 4, 1, 1, 3, 2, 2, 1, 3, 1, 2

19. Question
What could we use as a simulation when the following ratios
are given:
a. 1:2 b. 1:4 c. 1:6

20. Question
What could we use as a simulation when the following ratios
are given:
a. 1:2 b. 1:4 c. 1:6
Coin

21. Question
What could we use as a simulation when the following ratios
are given:
a. 1:2 b. 1:4 c. 1:6
Coin
Cards

22. Question
What could we use as a simulation when the following ratios
are given:
a. 1:2 b. 1:4 c. 1:6
Coin
Cards
Dice

23. Question
What could we use as a simulation when the following ratios
are given:
a. 1:2 b. 1:4 c. 1:6
Coin
Cards
Dice
Spinner

24. Question
What could we use as a simulation when the following ratios
are given:
a. 1:2 b. 1:4 c. 1:6
Coin Cards
Cards
Dice
Spinner

25. Question
What could we use as a simulation when the following ratios
are given:
a. 1:2 b. 1:4 c. 1:6
Coin Cards
Cards Spinner
Dice
Spinner

26. Question
What could we use as a simulation when the following ratios
are given:
a. 1:2 b. 1:4 c. 1:6
Coin Cards Dice
Cards Spinner
Dice
Spinner

27. Question
What could we use as a simulation when the following ratios
are given:
a. 1:2 b. 1:4 c. 1:6
Coin Cards Dice
Cards Spinner Spinner
Dice
Spinner

28. Problem Set

29. Problem Set
p. 155 #1-10 all, 11-25 odd
“If you tell the truth you don’t have to remember anything.”
- Mark Twain