Possible Outcomes. red. green
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1 . 7.10A STUDENT ACTIVITY #1 Problem #1: Bianca is conducting an experiment that involves removing color tiles from a bag containing these color tiles: 3 red, 2 green, and 1 yellow. What are all the possible outcomes when one tile is removed and not replaced and then another tile is removed? Use the table below to display all the possible outcomes for this experiment. Possible Outcomes First Tile red Second Tile green The outcome and is not possible, because there is only yellow tile. Once the yellow tile is removed, it is not possible to pick another tile. There are a total of possible outcomes for this experiment. Make a sample space list of the possible outcomes for this experiment in the space below: The sample space shows there are possible outcomes for this experiment. TEKSING TOWARD TAKS Weeks 5 - Lesson 4 Page 1
2 Problem #2: Carlos has six marbles of three different colors: 2 white, 3 black, and 1 red. What are all the possible outcomes when one marble is removed and replaced and then another marble is removed? Create a sample space tree diagram that shows all the possible outcomes for this series of events. Use the space below to show your tree diagram. The tree diagram shows a total of possible outcomes for this series of events. Use the table below to display all the possible outcomes for this series of events. Possible Outcomes First Marble Second Marble The table shows a total of possible outcomes for this series of events. Describe the difference between the outcomes in Problem #1 and Problem #2. TEKSING TOWARD TAKS Weeks 5 - Lesson 4 Page 2
3 Problem #3: Hermelinda conducted an experiment with these 8 letter tiles. V O A T F Q Q A She turned the tiles face down and chose 2 tiles at random. What are the possible outcomes? Construct a sample space list for the experiment. Display the list in the space below. The list shows a total of possible outcomes for this series of events. Construct a table for the experiment. Display the table in the space below. The table shows a total of possible outcomes for this experiment. TEKSING TOWARD TAKS Weeks 5 - Lesson 4 Page 3
4 7.10A STUDENT ACTIVITY #2 Problem #1: A movie theatre provides its workers with several choices of uniform. Shirts come in yellow, red, blue, and white. Shorts come in black, navy, and gray. How many uniform combinations are possible for the theatre workers? What sample space shows all the possible outcomes for this event? Use the lines below to show the sample space. Shirt, shorts Shirt, shorts Shirt, shorts,,,,,,,,,,,, There are a total of possible uniform combinations for the theatre workers. Are the outcomes in this event dependent or independent events? Justify your answer. Problem #2: A sporting good store sells several brands of golf club sets and golf balls. Golf club sets include Nike, Tiger Woods, Classic, and Byron Nelson. Golf balls include Nike, Flight, and Fly High. How many combinations of golf club sets and golf balls are possible? Create a sample space to show all the possible outcomes for this event. Use the space below to show your sample space. There are a total of possible combinations for the golf club sets and golf balls Are the outcomes in this event dependent or independent events? Justify your answer. TEKSING TOWARD TAKS Weeks 5 - Lesson 4 Page 4
5 Problem #3: Peg has four tiles of different colors: 2 white, 1 black, and 1 red. She randomly chooses two tiles at the same time. What are all the possible outcomes for this event? Create a sample space that shows all the possible outcomes for this event. Use the space below to show your sample space. There are a total of possible combinations for the tiles.. Problem #4: For his lunch Lee can choose from three types of sandwiches: chicken, ham, or peanut butter. He can choose from two drinks: milk or juice. What are all the possible combinations for Lee s lunch? Make a list that shows all the possible combinations of sandwiches and drinks Lee can choose for lunch. Use the space below to show list. There are a total of possible sandwich and drink combinations for Lee to choose. Are the outcomes in this event dependent or independent events? Justify your answer. TEKSING TOWARD TAKS Weeks 5 - Lesson 4 Page 5
6 7.10A STUDENT ACTIVITY #3 Materials: 5 student name cards in a gallon baggie, Student Activity #3 Problem: How can you make an organized list of all the possible combinations for this event? Procedure: Work in partner pairs. Scenario: Each six weeks the principal at South Middle School places the names of the students who have perfect attendance into a fish bowl and draws names for two available prizes. The students who have perfect attendance this month are Jessica, Gerard, Monica, Casey, and Sam. The prizes are two mountain bikes donated by a local bicycle shop. What are all the possible outcomes of the drawing? Use the student name cards in the baggie to model the event without replacement. Make an organized list of the possible outcomes from the model of the event in the space below. Be sure to mark out any outcomes that are the same as another outcome. For example, drawing Jessica then Gerard is the same as drawing Gerard then Jessica. The outcome is the same both students will get a mountain bike. How do you know you have correctly listed all the possible outcomes? Describe the process you used to model the event without replacement and make the sample space list. TEKSING TOWARD TAKS Weeks 5 - Lesson 4 Page 6
7 Use the student name cards in the baggie to model the event with replacement. Make an organized list of the possible outcomes from the model of the event in the space below. How do you know you have correctly listed all the possible outcomes? Describe the process you used to model the event with replacement and make the sample space list. Explain the difference between the possible outcomes when the event is conducted with and without replacement? Based on your sample space, record the probability of each student winning the prize without replacement in the table below. Student Probability TEKSING TOWARD TAKS Weeks 5 - Lesson 4 Page 7
8 Based on your sample space, record the probability of each student winning the prize with replacement in the table below. Student Probability What is the probability of a student winning both prizes when the event occurs without replacement? Explain your answer. What is the probability a student winning both prizes when the event occurs with replacement? Explain your answer. The principal has asked your advice about conducting the event with or without replacement. Your name is one of those in the drawing. What advice would you give to make your chances better for winning a bike? Justify your answer. What advice would you give it the principal asked you whether to conduct the event with or without replacement if he wants to make the drawing as fair as possible? Explain your answer. TEKSING TOWARD TAKS Weeks 5 - Lesson 4 Page 8
9 7.10A OPEN ENDED #1 Problem #1: Simon has 2 nickels, 4 dimes and 1 penny in his pocket. He randomly selects three of the coins. List all the unique outcomes. Problem #2: Joseph has a bag of colored marbles. It contains 3 yellow, 4 white and 1 blue. He selects one marble without replacing it, and then selects a second marble. List all the unique outcomes. 1. What mathematical concepts and vocabulary do I need to know to be able to work these problems? 2. Will the Grade 7 Mathematics Formula Chart be helpful on these problems? Why or why not? 3. Will a picture or diagram be helpful on these problems? Why or why not? 4. What problem-solving strategy or strategies will I use to help solve these problems? 5. Extension (7.10A): If Mary adds two green marbles to the bag before Joseph selects his marbles, how will the outcomes change? TEKSING TOWARD TAKS Weeks 5 - Lesson 4 Page 9
10 7.10A OPEN ENDED #2 Barney has a bag that contains 3 red marbles, 1 green marble and 4 blue marbles. He draws out 2 marbles at one time. Draw a sample space to show all the unique outcomes for his draw. 1. What mathematical concepts and vocabulary do I need to know to be able to work this problem? 2. Will the Grade 7 Mathematics Formula Chart be helpful on this problem? Why or why not? 3. How can I organize my list to help me be sure I have listed all of the unique outcomes? 4. Is a green and blue outcome the same as a blue and green outcome? Explain. 5. What problem-solving strategy or strategies will I use to help solve this problem? 6. Extension (7.10A): If Barney removes one of the blue marbles and replaces it with a yellow marble, how many unique outcomes will he have for drawing 2 marbles at a time? TEKSING TOWARD TAKS Weeks 5 - Lesson 4 Page 10
11 NAME DATE SCORE /5 7.10A Homework #1 1. Mary tosses a nickel, a dime and a penny. Make a table to show all the unique outcomes of this experiment. Are the outcomes of this experiment dependent or independent events? Explain your answer. 2. Marty has a bag that contains colored candies. It has 4 red, 2 green, 4 yellow and 3 blue pieces of candy. If he reaches in and randomly selects 2 pieces of candy, what are all the possible outcomes? Are the outcomes of this event independent or dependent? Show your work and explain your answer. 3. Jose is playing a game that has three spinners. The spinners are shown below. A B B A $ # Spinner 1 Spinner 2 Spinner 3 Make a table that shows all the possible combinations of an A or B on Spinner 1, a $ on Spinner 2 and an odd number on Spinner 3. Are the outcomes of this event dependent or independent? Explain your answer. TEKSING TOWARD TAKS Weeks 5 - Lesson 4 Page 11
12 4. For lunch Maria can choose from three types of pizza: hamburger, pepperoni, or cheese. She can choose from three drinks: milk, water, or juice. Make a list that shows all the possible combinations Maria can choose for lunch if she wants one slice of pizza and one drink. Are the outcomes of this event independent or dependent? Explain your answer. 5. Roberto was using the digits, 1, 3, 5, and 7, to create two-digit numbers. He was not allowed to use a digit more than once to create each two-digit number. Make a tree diagram that shows all of the possible two-digit numbers that begin with a 5. Are the outcomes of this event independent or dependent? Explain your answer. TEKSING TOWARD TAKS Weeks 5 - Lesson 4 Page 12
13 NAME DATE SCORE /5 7.10A Homework #2 1. Betsy spins the spinner below three times in an experiment. She spins a one on the first spin. Make a table to show the possible outcomes for the three spins. Are the outcomes of this experiment dependent or independent events? Explain your answer William flips a nickel, a dime, and a quarter. Make a table to show all the possible outcomes of his experiment. Are the outcomes of this experiment dependent or independent events? Explain your answer. 3. Micah used the digits 4, 5 and 6 to make three-digit numbers that are larger than 500. She used each digit only once to make each of the three-digit numbers. Make a tree diagram to shows all the possible three-digit numbers that are larger than 500. Are the outcomes dependent or independent events? Explain your answer. TEKSING TOWARD TAKS Weeks 5 - Lesson 4 Page 13
14 4. Brandon is playing a game that involves removing color tiles from a bag containing these color tiles: 2 red, 3 blue, and 1 yellow. What are all the possible outcomes when one tile is removed and not replaced and then another tile is removed? Make a chart to show the possible outcomes. Are the outcomes dependent or independent events? Explain your answer. 5. For her lunch Tiffany can choose from three types of soup: chicken noodle, vegetable beef, or tomato. She can choose from two types of bread: wheat roll or cornbread. Make a list that shows all the possible combinations of soups and breads Tiffany can choose for lunch. Use the space below to show list. Are the outcomes dependent or independent events? Explain your answer. TEKSING TOWARD TAKS Weeks 5 - Lesson 4 Page 14
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