Review for Test 2 - What Are the Odds? Multiple Choice Identify the choice that best completes the statement or answers the question. ____

1. A spinner that has 5 sections of equal area, numbered from 1 to 5, is spun two times in succession. Which is NOT part of the sample space? a. (1, 3) b. (4, 3) c. (1, 6) d. (5, 1)

Short Answer 2. For two weeks, Mark recorded the color of the traffic light at the intersection of Main Street and North Avenue as his school bus approached the intersection. The results were: green, red, red, red, red, red, green, red, red, yellow. Make a frequency table for the data.

3. Use the frequency table. Find the probability that a person goes to the movies at least 2 times a month. Round to the nearest thousandth.

Trips to the Movies Number of Movies More than 7 movies per month 5–7 movies per month 2–4 movies per month Less than 2 movies per month Total

Number of Moviegoers 103 177 256 199 735

4. The dartboard has 8 sections of equal area. The letters represent the colors red (R), yellow (Y), blue (B), and green (G). Use a table to show the probability distribution for a dart that hits the board at a random location.

R

G

G

G

G

Y B

R

5. The table shows the results of a survey of students in two math classes. Find P(more than 1 hour of TV | 6th period class). Round to the nearest thousandth. Did You Watch More Than One Hour of TV Last Night? Yes No 10 5 3rd period class 9 10 6th period class

6. The table shows the results of a survey of college students. Find the probability that a student’s first class of the day is a humanities class, given the student is male. Round to the nearest thousandth. First Class of the Day for College Students Male Female 80 60 Humanities 90 50 Science 85 75 Other

7. Each person in a group of students was identified by year and asked when he or she preferred taking classes: in the morning, afternoon, or evening. The results are shown in the table. Find the probability that the student preferred afternoon classes given he or she is a junior. Round to the nearest thousandth. When Do You Prefer to Take Classes? Freshman Sophomore 7 13 Morning 7 16 Afternoon 8 16 Evening

Junior 19 6 5

Senior 20 18 15

8. The probability that a city bus is ready for service when needed is 86%. The probability that a city bus is ready for service and has a working radio is 69%. Find the probability that a bus chosen at random has a working radio given that it is ready for service. Round to the nearest tenth of a percent.

Find the mean, median, and mode of the data set. Round to the nearest tenth. 9. 7, 15, 8, 10, 9, 1, 4, 11, 14, 14, 14

10. test scores on a math exam: 87, 76, 77, 98, 69, 97, 70, 65, 85, 89, 65, 84, 75, 92, 88, 85, 98, 88, 64, 88, 64, 97

Make a box-and-whisker plot of the data. 11. 27, 23, 22, 28, 16, 14, 28, 11

12. average daily temperatures in Tucson, Arizona, in December: 57, 57, 65, 51, 49, 66, 58, 50, 55, 51, 60, 58, 60, 63, 54, 62, 59, 66, 60, 49

Find the outlier in the set of data.

13. 5.8, 5.7, 4.5, 0.3, 4.4, 4.2, 4.9, 6.3

14. 20, 35, 11, 23, 14, 19, 17, 16

15. In your last 23 basketball games, you attempted 95 free throws and made 60. Find the experimental probability that you make a free throw. Write the probability as a percent, to the nearest tenth of a percent.

16. A number cube is rolled with these results: 71 ones, 71 twos, 62 threes, 72 fours, 51 fives, and 54 sixes. What is the experimental probability of rolling an even number? Write your answer as a percent, to the nearest tenth of a percent.

17. You work at a T-shirt printing business. Of the 4,400 T-shirts shipped, 633 have a defect. What is the experimental probability that a T-shirt has a defect? Write your answer as a percent, to the nearest tenth of a percent.

18. Find the range of the data. Scores: 90, 99, 92, 90, 97, 80, 86, 97, 83, 93

Draw the box-and-whisker plot for the data. 19. 41, 34, 43, 42, 25, 27, 26, 26, 48, 50, 35, 50, 28, 25, 43

20. Find the sample space for tossing 4 coins. Then find P(exactly 2 heads).

21. Jason and Kyle both choose a number from 1 to 22 at random. What is the probability that both numbers are odd?

22. A drawer contains 2 red socks, 3 white socks, and 5 blue socks. Without looking, you select a sock at random, replace it, and select a second sock at random. What is the probability that the first sock is blue and the second sock is red?

23. A bag contains 8 purple marbles and 4 white marbles. One marble is drawn at random and not replaced. Then a second marble is drawn at random. What is the probability that the first marble is white and the second one is purple?

24. In how many different ways can you arrange 5 books on a shelf?

Simplify the expression. 25.

26.

27.

28.

29. Participants in a study of a new medication received either medication A or a placebo. Make a tree diagram of the results of the study. Then find P(placebo and improvement). Of all those who participated in the study, 85% received medication A. Of those who received medication A, 67% reported an improvement. Of those who received the placebo, 75% reported no improvement.

Essay 30. A study of traffic patterns in a large city shows that if the weather is rainy, there is a 50% chance of an automobile accident occurring during the morning commute. If the weather is clear, the chance of an accident is reduced to 25%. Suppose the weather forecast for tomorrow predicts a 65% chance of rain. a. Draw a tree diagram based on the information. b. Find P(it will rain tomorrow and there will be an accident). Show your work. c. Find P(there will be an accident tomorrow). Show your work.

Review for Test 2 - What Are the Odds? Answer Section MULTIPLE CHOICE 1. ANS: REF: OBJ: STA: KEY:

C PTS: 1 DIF: L3 12-4 Counting Outcomes and Theoretical Probability 12-4.2 Finding Probability by Counting Outcomes NAT: NAEP 2005 D4b | NAEP 2005 D4e 8MI D.PR.08.04 TOP: 12-4 Example 3 sample space

SHORT ANSWER 2. ANS:

PTS: 1 DIF: L2 REF: 12-1 Probability Distributions OBJ: 12-1.1 Making a Probability Distribution NAT: CAT5.LV21/22.45 | CAT5.LV21/22.46 | CAT5.LV21/22.51 | CAT5.LV21/22.53 | IT.LV17/18.CP | IT.LV17/18.DI | IT.LV17/18.DP | IT.LV17/18.FR | S9.TSK3.DSP | S9.TSK3.NS | S10.TSK3.DSP | S10.TSK3.NS | TV.LV21/22.11 | TV.LV21/22.12 | TV.LV21/22.15 | TV.LV21/22.47 | TV.LVALG.53 | TV.LVALG.56 | ADP L.4.2 | ADP L.4.5 STA: MI S4.1.3 TOP: 12-1 Example 1 KEY: frequency table 3. ANS: 0.729 PTS: 1 DIF: L2 REF: 12-1 Probability Distributions OBJ: 12-1.1 Making a Probability Distribution NAT: CAT5.LV21/22.45 | CAT5.LV21/22.46 | CAT5.LV21/22.51 | CAT5.LV21/22.53 | IT.LV17/18.CP | IT.LV17/18.DI | IT.LV17/18.DP | IT.LV17/18.FR | S9.TSK3.DSP | S9.TSK3.NS | S10.TSK3.DSP | S10.TSK3.NS | TV.LV21/22.11 | TV.LV21/22.12 | TV.LV21/22.15 | TV.LV21/22.47 | TV.LVALG.53 | TV.LVALG.56 | ADP L.4.2 | ADP L.4.5 STA: MI S4.1.3 TOP: 12-1 Example 2 KEY: frequency table | cumulative probability 4. ANS:

PTS: 1

DIF: L2

REF: 12-1 Probability Distributions

OBJ: 12-1.1 Making a Probability Distribution NAT: CAT5.LV21/22.45 | CAT5.LV21/22.46 | CAT5.LV21/22.51 | CAT5.LV21/22.53 | IT.LV17/18.CP | IT.LV17/18.DI | IT.LV17/18.DP | IT.LV17/18.FR | S9.TSK3.DSP | S9.TSK3.NS | S10.TSK3.DSP | S10.TSK3.NS | TV.LV21/22.11 | TV.LV21/22.12 | TV.LV21/22.15 | TV.LV21/22.47 | TV.LVALG.53 | TV.LVALG.56 | ADP L.4.2 | ADP L.4.5 STA: MI S4.1.3 TOP: 12-1 Example 3 KEY: probability distribution 5. ANS: 0.474 PTS: 1 DIF: L2 REF: 12-2 Conditional Probability OBJ: 12-2.1 Finding Conditional Probabilities NAT: NAEP D4e | NAEP D4i | CAT5.LV21/22.45 | CAT5.LV21/22.46 | CAT5.LV21/22.51 | CAT5.LV21/22.53 | IT.LV17/18.CP | IT.LV17/18.DI | IT.LV17/18.DP | IT.LV17/18.FR | S9.TSK3.DSP | S9.TSK3.NS | S10.TSK3.DSP | S10.TSK3.NS | TV.LV21/22.11 | TV.LV21/22.12 | TV.LV21/22.15 | TV.LV21/22.47 | TV.LVALG.53 | ADP L.4.2 | ADP L.4.4 | ADP L.4.5 STA: MI S4.1.2 | MI S4.2.1 | MI S4.2.2 TOP: 12-2 Example 1 KEY: conditional probability 6. ANS: 0.314 PTS: 1 DIF: L2 REF: 12-2 Conditional Probability OBJ: 12-2.1 Finding Conditional Probabilities NAT: NAEP D4e | NAEP D4i | CAT5.LV21/22.45 | CAT5.LV21/22.46 | CAT5.LV21/22.51 | CAT5.LV21/22.53 | IT.LV17/18.CP | IT.LV17/18.DI | IT.LV17/18.DP | IT.LV17/18.FR | S9.TSK3.DSP | S9.TSK3.NS | S10.TSK3.DSP | S10.TSK3.NS | TV.LV21/22.11 | TV.LV21/22.12 | TV.LV21/22.15 | TV.LV21/22.47 | TV.LVALG.53 | ADP L.4.2 | ADP L.4.4 | ADP L.4.5 STA: MI S4.1.2 | MI S4.2.1 | MI S4.2.2 TOP: 12-2 Example 2 KEY: conditional probability 7. ANS: 0.200 PTS: 1 DIF: L3 REF: 12-2 Conditional Probability OBJ: 12-2.1 Finding Conditional Probabilities NAT: NAEP D4e | NAEP D4i | CAT5.LV21/22.45 | CAT5.LV21/22.46 | CAT5.LV21/22.51 | CAT5.LV21/22.53 | IT.LV17/18.CP | IT.LV17/18.DI | IT.LV17/18.DP | IT.LV17/18.FR | S9.TSK3.DSP | S9.TSK3.NS | S10.TSK3.DSP | S10.TSK3.NS | TV.LV21/22.11 | TV.LV21/22.12 | TV.LV21/22.15 | TV.LV21/22.47 | TV.LVALG.53 | ADP L.4.2 | ADP L.4.4 | ADP L.4.5 STA: MI S4.1.2 | MI S4.2.1 | MI S4.2.2 TOP: 12-2 Example 2 KEY: conditional probability 8. ANS: 80.2% PTS: 1 DIF: L2 REF: 12-2 Conditional Probability OBJ: 12-2.2 Using Formulas and Tree Diagrams NAT: NAEP D4e | NAEP D4i | CAT5.LV21/22.45 | CAT5.LV21/22.46 | CAT5.LV21/22.51 | CAT5.LV21/22.53 | IT.LV17/18.CP | IT.LV17/18.DI | IT.LV17/18.DP | IT.LV17/18.FR | S9.TSK3.DSP | S9.TSK3.NS | S10.TSK3.DSP | S10.TSK3.NS | TV.LV21/22.11 | TV.LV21/22.12 | TV.LV21/22.15 | TV.LV21/22.47 | TV.LVALG.53 | ADP L.4.2 | ADP L.4.4 | ADP L.4.5 STA: MI S4.1.2 | MI S4.2.1 | MI S4.2.2 TOP: 12-2 Example 3 KEY: conditional probability | word problem | problem solving

9. ANS: mean = 9.7, median = 10, mode = 14 PTS: 1 DIF: L2 REF: 12-3 Analyzing Data OBJ: 12-3.1 Measures of Central Tendency NAT: NAEP D1b | NAEP D1d | NAEP D2a | CAT5.LV21/22.47 | CAT5.LV21/22.51 | CAT5.LV21/22.53 | IT.LV17/18.CP | IT.LV17/18.DI | IT.LV17/18.I | IT.LV17/18.PS | S9.TSK3.DSP | S9.TSK3.NS | S10.TSK3.DSP | S10.TSK3.NS | TV.LV21/22.15 | TV.LV21/22.17 | TV.LV21/22.49 | TV.LVALG.53 | ADP I.4.2 | ADP L.1.1 | ADP L.1.2 | ADP L.1.3 STA: MI S1.1.1 | MI S1.2.1 | MI S1.2.3 TOP: 12-3 Example 1 KEY: mean | median | mode 10. ANS: mean = 81.9, median = 85, mode = 88 PTS: 1 DIF: L2 REF: 12-3 Analyzing Data OBJ: 12-3.1 Measures of Central Tendency NAT: NAEP D1b | NAEP D1d | NAEP D2a | CAT5.LV21/22.47 | CAT5.LV21/22.51 | CAT5.LV21/22.53 | IT.LV17/18.CP | IT.LV17/18.DI | IT.LV17/18.I | IT.LV17/18.PS | S9.TSK3.DSP | S9.TSK3.NS | S10.TSK3.DSP | S10.TSK3.NS | TV.LV21/22.15 | TV.LV21/22.17 | TV.LV21/22.49 | TV.LVALG.53 | ADP I.4.2 | ADP L.1.1 | ADP L.1.2 | ADP L.1.3 STA: MI S1.1.1 | MI S1.2.1 | MI S1.2.3 TOP: 12-3 Example 2 KEY: mean | median | mode 11. ANS:

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

PTS: 1 DIF: L2 REF: 12-3 Analyzing Data OBJ: 12-3.2 Box-and-Whisker Plots NAT: NAEP D1b | NAEP D1d | NAEP D2a | CAT5.LV21/22.47 | CAT5.LV21/22.51 | CAT5.LV21/22.53 | IT.LV17/18.CP | IT.LV17/18.DI | IT.LV17/18.I | IT.LV17/18.PS | S9.TSK3.DSP | S9.TSK3.NS | S10.TSK3.DSP | S10.TSK3.NS | TV.LV21/22.15 | TV.LV21/22.17 | TV.LV21/22.49 | TV.LVALG.53 | ADP I.4.2 | ADP L.1.1 | ADP L.1.2 | ADP L.1.3 STA: MI S1.1.1 | MI S1.2.1 | MI S1.2.3 TOP: 12-3 Example 3 KEY: median | quartile | box-and-whisker plot 12. ANS:

48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68

PTS: 1 DIF: L2 REF: 12-3 Analyzing Data OBJ: 12-3.2 Box-and-Whisker Plots NAT: NAEP D1b | NAEP D1d | NAEP D2a | CAT5.LV21/22.47 | CAT5.LV21/22.51 | CAT5.LV21/22.53 | IT.LV17/18.CP | IT.LV17/18.DI | IT.LV17/18.I | IT.LV17/18.PS | S9.TSK3.DSP | S9.TSK3.NS | S10.TSK3.DSP | S10.TSK3.NS | TV.LV21/22.15 | TV.LV21/22.17 | TV.LV21/22.49 | TV.LVALG.53 | ADP I.4.2 | ADP L.1.1 | ADP L.1.2 | ADP L.1.3 STA: MI S1.1.1 | MI S1.2.1 | MI S1.2.3 TOP: 12-3 Example 4 KEY: median | quartile | box-and-whisker plot 13. ANS: 0.3 PTS: 1 DIF: L2 REF: 12-3 Analyzing Data OBJ: 12-3.2 Box-and-Whisker Plots NAT: NAEP D1b | NAEP D1d | NAEP D2a | CAT5.LV21/22.47 | CAT5.LV21/22.51 | CAT5.LV21/22.53 |

IT.LV17/18.CP | IT.LV17/18.DI | IT.LV17/18.I | IT.LV17/18.PS | S9.TSK3.DSP | S9.TSK3.NS | S10.TSK3.DSP | S10.TSK3.NS | TV.LV21/22.15 | TV.LV21/22.17 | TV.LV21/22.49 | TV.LVALG.53 | ADP I.4.2 | ADP L.1.1 | ADP L.1.2 | ADP L.1.3 STA: MI S1.1.1 | MI S1.2.1 | MI S1.2.3 TOP: 12-3 Example 6 KEY: outlier 14. ANS: 35 PTS: 1 DIF: L2 REF: 12-3 Analyzing Data OBJ: 12-3.2 Box-and-Whisker Plots NAT: NAEP D1b | NAEP D1d | NAEP D2a | CAT5.LV21/22.47 | CAT5.LV21/22.51 | CAT5.LV21/22.53 | IT.LV17/18.CP | IT.LV17/18.DI | IT.LV17/18.I | IT.LV17/18.PS | S9.TSK3.DSP | S9.TSK3.NS | S10.TSK3.DSP | S10.TSK3.NS | TV.LV21/22.15 | TV.LV21/22.17 | TV.LV21/22.49 | TV.LVALG.53 | ADP I.4.2 | ADP L.1.1 | ADP L.1.2 | ADP L.1.3 STA: MI S1.1.1 | MI S1.2.1 | MI S1.2.3 TOP: 12-3 Example 6 KEY: outlier 15. ANS: 63.2% PTS: 1 DIF: L2 REF: 12-7 Experimental Probability OBJ: 12-7.1 Finding Experimental Probability NAT: NAEP 2005 D4d TOP: 12-7 Example 1 KEY: experimental probability 16. ANS: 51.7% PTS: 1 DIF: L3 REF: 12-7 Experimental Probability OBJ: 12-7.1 Finding Experimental Probability NAT: NAEP 2005 D4d TOP: 12-7 Example 1 KEY: experimental probability 17. ANS: 14.4% PTS: 1 DIF: L2 REF: 12-7 Experimental Probability OBJ: 12-7.1 Finding Experimental Probability NAT: NAEP 2005 D4d TOP: 12-7 Example 1 KEY: experimental probability 18. ANS: 19 PTS: 1 DIF: L2 REF: 12-1 Data Analysis and Probability OBJ: 12-1.2 Using Line Plots to Display Data NAT: NAEP 2005 D1b | NAEP 2005 D1d TOP: 12-1 Example 2 KEY: line plot | range 19. ANS:

25

30

35

40

45

50

PTS: 1 DIF: L2 REF: 12-2 Box-and-Whisker Plots OBJ: 12-2.1 Making Box-and-Whisker Plots NAT: NAEP 2005 D2b | NAEP 2005 D2d TOP: 12-2 Example 1 KEY: box-and-whisker plot 20. ANS: 3 8

PTS: OBJ: STA: KEY: 21. ANS:

1 DIF: L2 REF: 12-4 Counting Outcomes and Theoretical Probability 12-4.2 Finding Probability by Counting Outcomes NAT: NAEP 2005 D4b | NAEP 2005 D4e 8MI D.PR.08.04 TOP: 12-4 Example 3 sample space | outcome | theoretical probability

PTS: OBJ: STA: KEY: 22. ANS: 1 10

1 DIF: L3 REF: 12-4 Counting Outcomes and Theoretical Probability 12-4.2 Finding Probability by Counting Outcomes NAT: NAEP 2005 D4b | NAEP 2005 D4e 8MI D.PR.08.04 TOP: 12-4 Example 4 theoretical probability | counting principle

PTS: 1 DIF: L2 OBJ: 12-5.1 Independent Events TOP: 12-5 Example 1 23. ANS: 8 33

REF: 12-5 Independent and Dependent Events NAT: NAEP 2005 D4a | NAEP 2005 D4h KEY: independent events

PTS: 1 DIF: L3 OBJ: 12-5.2 Dependent Events TOP: 12-5 Example 3 24. ANS: 120 ways

REF: 12-5 Independent and Dependent Events NAT: NAEP 2005 D4a | NAEP 2005 D4h KEY: dependent events

PTS: 1 DIF: L2 OBJ: 12-6.1 Permutations KEY: permutation 25. ANS: 24

REF: 12-6 Permutations and Combinations TOP: 12-6 Example 1

PTS: 1 DIF: L2 OBJ: 12-6.1 Permutations KEY: permutation 26. ANS: 3,628,800

REF: 12-6 Permutations and Combinations TOP: 12-6 Example 2

PTS: 1 DIF: L3 OBJ: 12-6.1 Permutations KEY: permutation 27. ANS: 7

REF: 12-6 Permutations and Combinations TOP: 12-6 Example 2

PTS: 1

DIF: L2

REF: 12-6 Permutations and Combinations

OBJ: 12-6.2 Combinations KEY: combinations 28. ANS: 220

TOP: 12-6 Example 4

PTS: 1 DIF: L3 OBJ: 12-6.2 Combinations KEY: combinations 29. ANS:

REF: 12-6 Permutations and Combinations TOP: 12-6 Example 4

P(placebo and improvement) = PTS: 1 DIF: L2 REF: 12-2 Conditional Probability OBJ: 12-2.2 Using Formulas and Tree Diagrams NAT: NAEP D4e | NAEP D4i | CAT5.LV21/22.45 | CAT5.LV21/22.46 | CAT5.LV21/22.51 | CAT5.LV21/22.53 | IT.LV17/18.CP | IT.LV17/18.DI | IT.LV17/18.DP | IT.LV17/18.FR | S9.TSK3.DSP | S9.TSK3.NS | S10.TSK3.DSP | S10.TSK3.NS | TV.LV21/22.11 | TV.LV21/22.12 | TV.LV21/22.15 | TV.LV21/22.47 | TV.LVALG.53 | ADP L.4.2 | ADP L.4.4 | ADP L.4.5 STA: MI S4.1.2 | MI S4.2.1 | MI S4.2.2 TOP: 12-2 Example 4 KEY: conditional probability | tree diagram ESSAY 30. ANS: [4] a.

0.5

Accident

Rain 0.65 0.5

No accident

0.25

Accident

0.35

Clear 0.75

No accident

b.

c.

[3] [2] [1]

one part incorrect two parts incorrect correct answers but no work shown

PTS: 1 DIF: L4 REF: 12-2 Conditional Probability OBJ: 12-2.2 Using Formulas and Tree Diagrams NAT: NAEP D4e | NAEP D4i | CAT5.LV21/22.45 | CAT5.LV21/22.46 | CAT5.LV21/22.51 | CAT5.LV21/22.53 | IT.LV17/18.CP | IT.LV17/18.DI | IT.LV17/18.DP | IT.LV17/18.FR | S9.TSK3.DSP | S9.TSK3.NS | S10.TSK3.DSP | S10.TSK3.NS | TV.LV21/22.11 | TV.LV21/22.12 | TV.LV21/22.15 | TV.LV21/22.47 | TV.LVALG.53 | ADP L.4.2 | ADP L.4.4 | ADP L.4.5 STA: MI S4.1.2 | MI S4.2.1 | MI S4.2.2 KEY: conditional probability | tree diagram | rubric-based question | extended response