North Carolina Math 2 Transition Edition Unit 6 Assessment: Probability

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1 Name: Class: _ Date: _ North Carolina Math Transition Edition Unit 6 Assessment: Probability Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Theresa chose a simple random sample of 60 students from the population of students taking world history. Juan chose a simple random sample of 30 students from the same population. Theresa and Juan then determined the mean grade point average of the students in each sample. Which of the following is true about the two sample means? a. The mean of Theresa s sample is a more reliable estimate of the population mean. b. There is less bias in Theresa s estimate. c. The mean of Juan s sample is a more reliable estimate of the population mean. d. There is less bias in Juan s estimate.. Suppose a simple random sample of 100 voters is chosen from the population of voters in which 43% are Democrat, 3% are Republican, and 5% are Independent. Which of the following is most improbable? a. Less than 30% of the voters in the sample are Democrat. b. Less than 30% of the voters in the sample are Republican. c. Less than 30% of the voters in the sample are Independent. d. All of the above are equally improbable. 3. How many ways can you roll a pair of six-sided dice and get an odd product? a. 7 c. 3 b. 18 d. 9 1

2 Name: 4. Tim has a bag that contains the following tiles. Tim takes a tile from the bag without looking. Then he replaces it. Then he takes another tile from the bag without looking. Consider the following events. LF: Tim takes L first. LS: Tim takes L second. LF and LS: Tim takes L first and L second. Which option describes the events? a. LF and LS are independent, and the probability of LF and LS is 4%. b. LF and LS are dependent, and the probability of LF and LS is 5%. c. LF and LS are dependent, and the probability of LF and LS is 4%. d. LF and LS are independent, and the probability of LF and LS is 5%. 5. The table shows data on 400 students at a college. Comparing Field of Study in College with High School Attended Field of study in college High school attended Science, math, Business or Social Visual and or engineering economics sciences performing arts Garfield Adams Washington Each pair of events below describes a student chosen randomly at the college. Which pair of events seems to be dependent, based on the data in the table? a. The student is in visual and performing arts and went to Garfield High School. b. The student is in visual and performing arts and went to Washington High School. c. The student is in visual and performing arts and went to Adams High School. d. The student is in social sciences and went to Adams High School.

3 Name: 6. Jennifer and Kia are in a basketball game. Prior to this game, Jennifer has made 14 free throws out of 0 attempts, and Kia has made 4 free throws out of 16 attempts. Jennifer is at the free-throw line, ready to shoot. Kia will attempt a free throw after Jennifer attempts hers. Based on their records, which option shows the best approximation of the probability that at least one of them will make the free throw? a. 5% c. 78% b. 50% d. 95% number of hits 7. The expression for calculating a baseball player s batting average is number of times at bat. Jorgen s batting average is 0.48, and he is at bat. Sven s batting average is 0.316, and he will be at bat after Jorgen. Assume that each player s performance is independent of the other s. What is the probability that Jorgen or Sven will get a hit, based on their batting averages? a. 0.8 c b d Which event has the least probability if 3 coins are tossed? a. exactly heads or exactly tails c. at least heads b. no head or exactly 1 head d. exactly 1 head or exactly tails 9. Peter spins spinner A and then spins spinner B. What is the probability that his first spin is even if the sum of his spins is odd? a. 0 c. b. 1 d

4 Name: 10. The Chambers have 3 puppies. Which pair of events is independent? a. The youngest puppy is a female. Exactly puppies are females. b. The middle puppy is a male. Exactly consecutive puppies are males. c. The youngest puppy is a male. Exactly consecutive puppies are females. d. The middle puppy is a female. At least puppies are females. 11. Green Ridge School is a combined middle school and high school. The cafeteria serves optional breakfast to high school students and then to middle school students. One morning the cafeteria served breakfast to 44 high school students and then 56 middle school students. Of those 100 breakfasts, 70 were breakfast tacos. Of the 70 breakfast tacos, 4 were served to high school students and 46 were served to middle school students. Consider the following events. T: A breakfast taco is served. MS: A middle school student is served. Which statement is true about events T and MS? a. Events T and MS are independent and P(T MS) = P(MS T). b. Events T and MS are independent and P(T MS) > P(MS T). c. Events T and MS are dependent and P(T MS) = P(MS T). d. Events T and MS are dependent and P(T MS) > P(MS T). 1. Brandon spins a spinner with equal sections 1 4 and then rolls a standard 6-sided number cube. What is the probability that the product of the spinner and number cube results is odd if the sum is even? a. 3 b. 1 d. c

5 Name: 13. A survey revealed that 56% of the students at West Ridge High School are involved in band. The survey also showed that 3% of the students at the school are involved in band and also participated in the fall 5K fund-raiser. What is the probability that a student who is involved in band also participated in the fall 5K fund-raiser? a. 67% c % b. 41.1% d. 33% 14. What is the probability that cards selected from a standard deck of 5 cards without replacement are both red? a c b d A college admissions officer was curious about the major chosen by students at his college who had graduated from three high schools in a nearby city. He collected data on a sample of students from those high schools. The table shows the data. High school College major Marine Science Pre-law Computer Science South Lake Red River Green Ridge The following probabilities apply to a randomly chosen student in the sample. Which probability is the greatest? a. the probability that a student went to Red River given that the student is a pre-law major b. the probability that a student went to South Lake given that the student is a marine science major c. the probability that a student is a marine science major given that the student went to Red River d. the probability that a student went to South Lake 5

6 Name: 16. The table below shows data about 104 pizzas sold in a pizzeria. Each pizza was sold with one topping. Pizza shape Pizza topping Green Pepper Mushroom Ham Pepperoni Round Square Consider the following events. G: A green pepper pizza is sold. M: A mushroom pizza is sold. H: A ham pizza is sold. P: A pepperoni pizza is sold. R: A round pizza is sold. S: A square pizza is sold. Which pair of events is independent? a. R and M c. R and H b. S and P d. none of these 17. A school librarian surveyed 40 students. He listed three novels and three movies, and asked the students to choose one from each category as their favorite. The table below shows the survey results. Favorite novel Favorite movie Nine Dogs Henry Porter Summerwater Total The Hidden Gnome Mosquito Nights Tomato Total Consider the following events, which apply to a randomly chosen student in the survey sample. MN: The student chose Mosquito Nights as his or her favorite novel. ND: The student chose Nine Dogs as his or her favorite movie. Which statement is true about events MN and ND? a. Events MN and ND are independent and P(MN ND) > P(ND MN). b. Events MN and ND are independent and P(MN ND) < P(ND MN). c. Events MN and ND are dependent and P(MN ND) < P(ND MN). d. Events MN and ND are dependent and P(MN ND) > P(ND MN). 6

7 Name: 18. A sports club for girls has 77 members. Each member is currently involved in one activity, as shown in the table. Grade Activity Basketball Cheerleading Softball The following probabilities apply to a randomly chosen member of the club. Which probability is the greatest? a. the probability that the girl is in the tenth grade, given that she is in softball b. the probability that the girl is in the tenth grade c. the probability that the girl is in the twelfth grade d. the probability that the girl is in the tenth grade, given that she is in cheerleading 19. The table below shows some data about a restaurant s pizza sales. Pizza size Crust Small Medium Large Thin Thick Consider the following events. THIN: A thin-crust is sold. S: A small pizza is sold. Which statement is true about events THIN and S? a. Events THIN and S are independent and P(THIN S) > P(S THIN) b. Events THIN and S are dependent and P(THIN S) < P(S THIN) c. Events THIN and S are dependent and P(THIN S) > P(S THIN) d. Events THIN and S are independent and P(THIN S) < P(S THIN) 7

8 Name: 0. Twin Lakes State Park has two popular hiking trails: Twisted Bend Trail and Falls Trail. On one particular day, 75 hiking groups used the trails: 30 groups used Twisted Bend Trail and 45 groups used Falls Trail. Of the 30 groups that used Twisted Bend Trail, 0 groups had children and 10 groups had no children. Of the 45 groups that used Falls Trail, 0 groups had children and 5 groups had no children.consider the following events. F: A hiking group uses Falls Trail. C: A hiking group has children. Which statement is true about events F and C? a. Events F and C are dependent and P(F C) = P(C F). b. Events F and C are independent and P(F C) = P(C F). c. Events F and C are independent and P(F C) > P(C F). d. Events F and C are dependent and P(F C) > P(C F). 8

9 North Carolina Math Transition Edition Unit 6 Assessment: Probability Answer Section MULTIPLE CHOICE 1. ANS: A PTS: 1 REF: MIII 1. NAT: S-IC. TOP: Populations Versus Random Samples and Random Sampling KEY: sample sampling simple random sample. ANS: A PTS: 1 REF: MIII 1. NAT: S-IC. TOP: Populations Versus Random Samples and Random Sampling KEY: sample sampling simple random sample 3. ANS: D PTS: 1 REF: MII 4.1 NAT: S-CP.1 TOP: Events KEY: sample space outcomes independent events 4. ANS: A PTS: 1 REF: MII 4.1 NAT: S-CP.1 TOP: Events KEY: sample space intersection 5. ANS: C PTS: 1 REF: MII 4.1 NAT: S-CP. TOP: Events KEY: independent events 6. ANS: C PTS: 1 REF: MII 4 NAT: S-CP. TOP: Applications of Probability KEY: probability Multiplication Rule MSC: Unit Assessment 7. ANS: C PTS: 1 REF: MII 4.1 NAT: S-CP.7 TOP: Events KEY: Addition Rule probability MSC: Pre-Assessment 8. ANS: D PTS: 1 REF: MII 4.1 NAT: S-CP.7 TOP: Events KEY: probability union independent events 9. ANS: C PTS: 1 REF: MII 4 NAT: S-CP.3 TOP: Applications of Probability KEY: probability sample space independent events event MSC: Unit Assessment 10. ANS: C PTS: 1 REF: MII 4. NAT: S-CP.5 KEY: conditional probability independent 11. ANS: D PTS: 1 REF: MII 4. NAT: S-CP.5 KEY: conditional probability independent 1. ANS: D PTS: 1 REF: MII 4. NAT: S-CP.6 KEY: conditional probability MSC: Pre-Assessment 1

10 13. ANS: B PTS: 1 REF: MII 4. NAT: S-CP.6 KEY: conditional probability 14. ANS: A PTS: 1 REF: MII 4. NAT: S-CP.6 KEY: conditional probability 15. ANS: A PTS: 1 REF: MII 4. NAT: S-CP.6 KEY: conditional probability two-way frequency table 16. ANS: A PTS: 1 REF: MII 4. NAT: S-CP.4 KEY: conditional probability two-way frequency table MSC: Pre-Assessment 17. ANS: C PTS: 1 REF: MII 4 NAT: S-CP.4 TOP: Applications of Probability KEY: probability two-way frequency table conditional probability independent events dependent events MSC: Unit Assessment 18. ANS: D PTS: 1 REF: MII 4. NAT: S-CP.4 KEY: conditional probability two-way frequency table MSC: Pre-Assessment 19. ANS: C PTS: 1 REF: MII 4. NAT: S-CP.4 KEY: conditional probability independent two-way frequency table 0. ANS: D PTS: 1 REF: MII 4. NAT: S-CP.5 KEY: conditional probability independent