Name: ______________________________________ Class: ______________ Date: ____________

Unit 6: Moving Straight Ahead

Investigation 4: Analyzing Compound Events Using an Area Model

Practice Ace Problems

Directions: Please complete the necessary problems to earn a maximum of 6 points according to the

chart below. Show all of your work clearly and neatly for credit- which will be earned based on

completion rather than correctness.

I can Understand, Find, and Design the Probabilities of Compound Events.

Lesson Practice problems Options Maximum Points

Lesson 1: Drawing Area Models to Find the Sample Space

1, 2, 3, 4, 5

3 Points

Lesson 2: One-and-One Free Throws: Simulating a Probability Situation

6, 7, 8, 9, 10, 11 4 Points

Lesson 3: Finding Expected Value

20, 21, 22 2 Points

______ / 9 Points

Name: ______________________________________ Class: ______________ Date: ____________

A school carnival committee features a different version of the Making Purple game, as shown

below.

1. Before play the game, do you predict that the school will make money on this game?

Explain.

2. Use an area model to show the possible outcomes for this game. Explain how your area

model shows all the possible outcomes.

3. What is the theoretical probability of choosing a red and a blue marble on one turn?

Name: ______________________________________ Class: ______________ Date: ____________

4. Suppose one marble is chosen from each bucket. Find the probability of each situation.

a. You choose a green marble from Bucket 1 and a yellow marble from Bucket 2.

b. You do not choose a blue marble from each bucket.

c. You choose two blue marbles.

d. You choose at least one blue marble.

5. Parker Middle School is having a Flag Day Festival. In a contest, students choose one block from each of two different bags. A student wins if he or she picks a red and a blue block. James makes the tree diagram below to find the probability of winning.

a. Draw an area model that represents this contest.

b. What is the probability of winning this contest?

Name: ______________________________________ Class: ______________ Date: ____________

6. There are two No- Cavity prize bins at a dentist’s office. One bin has two hot-pink

toothbrushes and three neon-yellow toothbrushes. The other bin has four packages of

sugar-free gum, three grapes and one strawberry. Kira has no cavities. The dentist tells her

to close her eyes and choose a prize from each bin.

a. What is the probability that Kira will choose a neon-yellow toothbrush and a pack of

grape gum? Draw an area model to support your solution.

b. The dental assistant refills the bins after every patient. Suppose the next 100

patients have no cavities. How many times do you expect the patients to get an eon-

yellow toothbrush and a pack of grape gum?

7. Bonita and Deion are using the spinners from the Making Purple game in Problem 4.2. They

take turns spinning. If the colors on the two spinners make purple, Deion scores. If the

colors do not make purple, Bonita scores. They want to make their game a fair game. How

many points should Deion score when the spinners make purple? How many points should

Bonita score when they do not make purple?

Name: ______________________________________ Class: ______________ Date: ____________

8. A science club hosts a carnival to raise money. A game called Making Purple at the carnival involves using both of the spinners shown. If the player gets red on spinner A and blue on spinner B, the player wins because mixing red and blue makes purple.

a. List the outcomes that are possible when you spin both pointers. Are the outcomes

equally likely? Explain your reasoning.

b. What is the theoretical probability that a player “makes purple”? Show or explain how you arrived at your answer.

c. If 100 people play the Making Purple game, how many people do you expect to win?

d. The club charges $1 per turn. A player who makes purple receives $5. The club expects 100 people to play. How much money do you expect the club to make.

For exercises 9-11, a bag contains three green marbles and two blue marbles. You choose a marble, return it to the bag, and then choose again.

9. a. Which method (make a tree diagram, make a list, use an area model, or make a table

or chart) would you use to find the possible outcomes? Explain your choice.

Name: ______________________________________ Class: ______________ Date: ____________

b. Use your chosen method to find all the possible outcomes.

10. Suppose you do this experiment 50 times. Predict the number of times you will choose two marbles of the same color. Use the method you chose in Exercise 9.

11. Suppose this experiment is a two person game. One marble score if the marbles match. The other player scores if the marbles do not match. Describe a scoring system that makes this a fair game.

Use the information in the table. It shows free-thrown statistics for some of the players on the basketball team.

Free-Thrown Statistics Name Free Throws Attempted Free Throws Made Gerrit 54 27 David 49 39 Ken 73 45 Alex 60 42

20.

a. Which player has the best chance of making his next free throw? Explain your reasoning.

b. What is the probability of making a free throw on the next try for each person?

Name: ______________________________________ Class: ______________ Date: ____________

21. a. Alex is in a one-and-one free-throw situation. What is the probability he will score 0

points? 1 point? 2 points?

b. Suppose Alex is in a one-and-one situation 100 times. How many times do you expect each outcome in part (a) to occur?

c. What is the average number of points you expect Alex to make in a one-and-one situation?

d. Repeat part (a) using Gerrit.

22. a. In a two-attempt free-throw situation, a player gets a second attempt even if the

first attempt is missed. Suppose Gerrit is in a two-attempt free-throw situation. What is the probability that he will score 0 points? 1 point? 2 points?

b. Compare your answers to Exercise 21. Explain why the answers are not exactly the same.