Unit 7 Sample Test Part 2: Probability of Compound Events, List, Tables, Tree.
Diagrams, and Simulations. 7.SP.8.a Understand that, just as with simple events,
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Name: ________________________ Class: ___________________ Date: __________
ID: A
Unit 7 Sample Test Part 2: Probability of Compound Events, List, Tables, Tree Diagrams, and Simulations 7.SP.8.a Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. 1. How many different 6-digit codes can be created if no digit is used more than once?
A standard deck of playing cards contains 52 cards. The deck is divided into 4 suits of 13 cards each: hearts, diamonds, clubs, and spades. Hearts and diamonds are red suits, and clubs and spades are black suits. Suppose a card is drawn from the deck and recorded. Then the card is reinserted into the deck, the deck is shuffled, and a second card is drawn and recorded. Find each probability. ____
2. P(2 spades) 1 a. 8 b.
____
1 17
d.
1 16
3. P(red card on the first draw, club on the second draw) 1 3 a. 8 c. 16 b.
____
1 4
c.
13 102
d.
1 2
4. P(black Ace on the first draw, red King on the second draw) 3 1 a. 511 c. 663 b.
1 676
d.
1 26
The drama club at Fairborn Middle School is putting on a play for parents, teachers, and students. The club is made up of the students shown in the table. Suppose one student is randomly selected to read an announcement for the play over the public address system. Find the probability of each event. Write as a fraction in simplest form. Boys 22 Girls 18 6th Graders 10 7th Graders 15 8th Graders 15 5. P(girl or boy)
6. P(7th grader or 8th grader)
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Name: ________________________
ID: A
7. A deli offers sub sandwiches on wheat or rye bread, with a choice of ham, salami, or turkey. The deli also offers customers a choice of American, Provolone, or Cheddar cheese. Suppose a sandwich is chosen at random. a. Make a tree diagram that shows all of the possible outcomes.
____
b.
What is the probability that a randomly selected sandwich will be ham on rye with American cheese?
c.
What is the probability that a randomly selected sandwich will contain Provolone cheese or salami?
8. Use the table which shows the results of rolling a numbered cube 25 times. Out of 125 rolls, how many outcomes would you expect to be 4? Number 1 2 3 a. b.
20 25
Rolls 2 5 4
Number 4 5 6
Rolls 7 3 4 c. d.
35 40
7.SP.8.b Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event. ____
9. The Pizza Palace offers 3 different styles of pizza and 8 different toppings. How many different single topping pizzas are possible? a. 24 pizzas c. 3 pizzas b. 11 pizzas d. 48 pizzas
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Name: ________________________
ID: A
____ 10. Mike’s suitcase contains 4 pairs of pants, 3 shirts, and 2 pairs of shoes. How many different outfits can he wear?
a. b.
20 outfits 9 outfits
c. d.
12 outfits 24 outfits
11. The area schools have a baseball tournament each year. Several schools participate. Of the teams below, what are the possible combinations for first and second place in the tournament? Bobcats
Lizards
Eagles
Cougars
12. Wan-ying, Edie, and Brandy rode together in a 4-seat rollercoaster at the local amusement park. The seating combinations included Front Right, Front Left, Rear Right, and Rear Left. Assuming the Front Left and Rear Left were never empty, what combination of seating was available to the three friends?
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Name: ________________________
ID: A
13. Alyssa is going to color this flag using three different colors: yellow, green, and red.
There are three parts to the flag: the background, Edge of Cross, and Inside of Cross. Part A How many different ways can she color the flag using all three colors?
Part B Complete this list of all of the different ways Alyssa could color the flag. Color of Background yellow
Color of Edge of Cross Color of Inside of Cross green red
14. Courtney is selling cookies as a fundraiser for her club. She has 5 kinds of cookies.
Part A If a customer buys 2 boxes of cookies, and the cookies are not of the same type, how many different combinations are possible? Part B Make an organized list of all the possible combinations.
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Name: ________________________
ID: A
15. Joseph, Sally, Chloe, Mario, Susan, and Lourdes are playing a game of tug of war with 3 players on each team. Joseph is the captain of Team A and Mario is the captain of Team B. List all of the combinations possible for the two teams.
16. Yu-Jun wants to buy some running clothes for the summer. The store has a special deal for one brand of running shoes, one T-shirt, and one pair of shorts. Shoe Brands Reebok Nike Adidas
Running Outfit Special T-Shirt Running Shorts Sleeveless Blue Short Sleeves Black
List all of the possible combinations that Yu-Jun could buy.
7.SP.8.c Design and use a simulation to generate frequencies for compound events. ____ 17. A number cube is tossed and the spinner below is spun. Find P(greater than 4 and A).
a.
1 3
c.
2 9
b.
4 9
d.
1 6
5
Name: ________________________
ID: A
____ 18. What is the probability of spinning (R) in expreriment A and spinning (G) in experiment B?
a. b.
3 25 1 6
c. d.
1 3 2 5
____ 19. What is the probability of rolling two number cubes and getting a number greater than 2 on each cube. 4 a. 9 c. 1 b.
1 36
d.
2 3
20. Students conducted the following experiment 50 times. They drew one card
from a box with some red cards and some black cards, put the card back in the box, and then drew another card. The results are shown in the table below. What is the experimental probability of drawing 2 black cards?
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ID: A
Unit 7 Sample Test Part 2: Probability of Compound Events, List, Tables, Tree Diagrams, and Simulations Answer Section 1. 151,200 codes
2. 3. 4. 5.
There are 10 ways to pick the first digit, 9 ways to pick the second digit, and so on. 10 · 9 · 8 · 7 · 6 · 5 = 151,200 D A B 1 Write the number of favorable outcomes over the total number of possible outcomes and simplify. 18 + 22 40 = 40 = 1 40
6.
3 4
Write the number of favorable outcomes over the total number of possible outcomes and simplify. 15 + 15 30 3 = 40 = 4 40
1
ID: A 7. a.
There are 18 possible outcomes: WHA, WHP, WHC, WSA, WSP, WSC, WTA, WTP, WTC, RHA, RHP, RHC, RSA, RSP, RSC, RTA, RTP, and RTC. b.
1 18
There is only 1 favorable outcome (RHA) out of 18 possible outcomes. c.
5 9
There are 10 outcomes that contain either Provolone cheese or salami (WHP, WSA, WSP, WSC, WTP, RHP, RSA, RSP, RSC, RTP). Write this over the total number of outcomes and simplify. 10 5 =9 18 Assessment Rubric Level 3 Superior *Shows thorough understanding of concepts. *Uses appropriate strategies. *Computation is correct. *Written explanation is exemplary. *Diagram/table/chart is accurate (as applicable). *Goes beyond requirements of problem. Level 2 Satisfactory *Shows understanding of concepts. *Uses appropriate strategies. *Computation is mostly correct. *Written explanation is effective. *Diagram/table/chart is mostly accurate (as applicable). *Satisfies all requirements of problem. Level 1 Nearly Satisfactory *Shows understanding of most concepts. *May not use appropriate strategies. *Computation is mostly correct. 2
ID: A *Written explanation is satisfactory. *Diagram/table/chart is mostly accurate (as applicable). *Satisfies most of the requirements of problem.
8. 9. 10. 11.
Level 0 Unsatisfactory *Shows little or no understanding of the concept. *May not use appropriate strategies. *Computation is incorrect. *Written explanation is not satisfactory. *Diagram/table/chart is not accurate (as applicable). *Does not satisfy requirements of problem. C A D Note: The following is only a sample answer. All reasonable answers should be accepted.
Combinations First Place Second Place Bobcats Lizards Bobcats Eagles Bobcats Cougars Lizards Bobcats Lizards Eagles Lizards Cougars Eagles Bobcats Eagles Lizards Eagles Cougars Cougars Bobcats Cougars Lizards Cougars Eagles 12. Note: The following is only a sample answer. All reasonable answers should be accepted. Front Left Wan-ying Wan-ying Wan-ying Wan-ying Edie Edie Edie Edie Brandy Brandy Brandy Brandy
Rear Left Edie Brandy Edie Brandy Wan-ying Brandy Wan-ying Brandy Wan-ying Edie Wan-ying Edie
Front Right Brandy Edie
Rear Right
Brandy Edie Brandy Wan-ying Brandy Wan-ying Edie Wan-ying Edie Wan-ying
3
ID: A 13. Note: The following is only a sample answer. All reasonable answers should be accepted. However, Part A must be correct. Part A There are 6 different combinations possible. Part B 1 2 3 4 5 6
Color of Background yellow yellow green green red red
Color of Edge of Cross green red yellow red green yellow
Color of Inside of Cross red green red yellow yellow green
14. Note: The following is only a sample answer. All reasonable answers should be accepted. However, Part A must be correct. Part A 10 Part B CO, CS, CP, CM, OS, OP, OM, SP, SM, PM KEY C = Chocolate Chip O = Oatmeal S = Sugar P = Peanut Butter M = Molasses 15. Note: The following is only a sample answer. All reasonable answers should be accepted. Team Combinations Joseph Joseph Joseph Joseph Joseph Joseph
Team A Sally Sally Sally Chloe Chloe Susan
Chloe Susan Lourdes Susan Lourdes Lourdes
Team B Susan Chloe Chloe Sally Sally Sally
Mario Mario Mario Mario Mario Mario
4
Lourdes Lourdes Susan Lourdes Susan Chloe
ID: A 16. Note: The following is only a sample answer. All reasonable answers should be accepted.
17. 18. 19. 20.
Combinations for Running Outfit Special Shoe Brands T-Shirt Running Shorts Reebok Sleeveless Blue Reebok Sleeveless Black Reebok Short Sleeves Blue Reebok Short Sleeves Black Nike Sleeveless Blue Nike Sleeveless Black Nike Short Sleeves Blue Nike Short Sleeves Black Adidas Sleeveless Blue Adidas Sleeveless Black Adidas Short Sleeves Blue Adidas Short Sleeves Black D A A 4 25
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Unit 7 Sample Test Part 2: Probability of Compound Events, List, Tables, Tree Diagrams, and Simulations [Answer Strip] D _____10.
A _____18.
D 2. _____ A _____19.
A _____ 3. C 8. _____
B _____ 4.
D _____17.
A _____ 9.
ID: A
