Math 10

2.23 If P(A) = 0.46, P(B) = 0.5, and A and B are mutually exclusive, find P(A or B).

A) 0 B) 0.48 C) 0.04 D) 0.96

3.15 The numbers 1 through 9 are written in separate slips of paper, and the slips are placed into a box. Then, 4 of these slips are drawn at random. What is the probability that the drawn slips are "1", "2", "3", and "4", in that order?

A) 0.00794 B) 0.19056 C) 0.007944 D) 0.000331

3.16 A committee consist of 8 women and 11 men. Three members are chosen as officers. What is the probability that all three officers are women?

A) 0.0578 B) 0.0746 C) 0.1703 D) 0.01243

2.25 If P(A) = 0.38, P(B) = 0.33, and P(A and B) = 0.24, find P(A or B).

A) 0.12 B) 0.355 C) 0.47 D) 0.24

2.29 A fair die is rolled four times. What is the probability that it comes up 1 at least once?

A) 0.1667 B) 0.8333 C) 0.4213 D) 0.5177

2.31 A fair die is rolled two times. What is the probability that both rolls are 1?

A) 0.167 B) 0.0046 term-67 C) 0.028 D) 0.083

2.32 According to popular belief, 80% of adults enjoy drinking beer. Choose a group of 4 adults at random. The probability that all of them enjoy drinking beer is:

A) 0.200 B) 0.410 C) 0.250 D) 3.200

2.22 In a recent semester at a local university, 500 students enrolled in both General Chemistry and Calculus I. Of these students, 66 received an A in general chemistry, 73 received an A in calculus, and 33 received an A in both general chemistry and calculus. Find the probability that a randomly chosen student received an A in general chemistry or calculus or both.

A) 0.278 B) 0.763 C) 0.344 D) 0.212

2.14 In a poll of 416 university students, 170 said that they were opposed to legalizing marijuana. What is the probability that a surveyed student opposes legalization of marijuana?

A) 0.409 B) 0.691 C) 0.309 D) 0.591

1.19 According to Chebyshev's theorem, the maximum proportion of data values from a data set that are more than 1.5 standard deviations from the mean is .

A) 0.44 B) 1.33 C) 0.17 D) 0.67

2.21 Out of 733 items checked out of a public library, 269 were fiction books, 222 were non-fiction books, and 242 were videos (of any genre). What is the probability that a randomly-selected item was not a video?

A) 0.67 B) 0.367 C) 0.33 D) 0.493

2.30 An unfair coin has a probability 0.6 of landing heads. The coin is tossed four times. What is the probability that it lands heads at least once?

A) 0.784 B) 0.9744 C) 0.25 D) 0.8704

2.28 Let A and B be events with P(A) = 0.5, P(B) = 0.4. Assume that A and B are independent. Find P(A and B).

A) 0.8 B) 0.5 C) 0.4 D) 0.2

1.18 A baseball player has a batting average of 0.325 each week of the season, with a standard deviation of 0.065. What is the z score when he bats 0.410 one week?

A) 1.308 B) 0.325 C) 1.275 D) 0.410

2.3 A baseball player has a batting average of 0.325 each week of the season, with a standard deviation of 0.065. What is the z score when he bats 0.410 one week?

A) 1.308 B) 1.275 C) 0.410 D) 0.325

2.10 If the probability that it will rain tomorrow is 0.39, what is the probability that it will not rain tomorrow?

A) 1.39 B) -0.39 C) 0.61 D) 0.39

1.14 A population has a mean = 21 and standard deviation = 11. Find the z-score for a population value of 40.

A) 1.7 B) 0.6 C) 19 D) 3.6

2.13 If two dice are rolled one time, find the probability of getting a sum of 6.

A) 1/12 B) 1/6 C) 5/36 D) 7/36

2.12 Find the probability of getting a number greater than 4 when a die is rolled one time.

A) 1/3 B) 1/2 C) 2/3 D) 1/6

3.13 If 20 tickets are sold and 2 prizes are to be awarded, find the probability that one person will win both prizes if that person buys exactly 2 tickets.

A) 1/380 B) 1/190 C) 1/480 D) 1/1140

2.17 At a certain college, there were 700 science majors, 300 engineering majors, and 500 business majors. If one student was selected at random, the probability that the student is an engineering major is

A) 1/4 B) 1/5 C) 4/5 D) 1/3

2.15 A section of an exam contains two multiple-choice questions, each with three answer choices (listed "A", "B", and "C"). Assuming the outcomes to be equally likely, find the probability (as a reduced fraction) that both answers are "C". [Hint: List all the outcomes of the sample space first.]

A) 1/6 B) 1/27 C) 1/9 D) 1/3

3.17 If 25 tickets are sold and 2 prizes are to be awarded, find the probability that one person will win both prizes if that person buys exactly 2 tickets.

A) 1/700 B) 1/2300 C) 1/600 D) 1/300

2.33 A coin is tossed 3 times. Find the probability that all 3 tosses are tails.

A) 1/8 B) 1/6 C) 1/3 D) 1/9

3.12 A bookcase contains 2 statistics books and 5 biology books. If 2 books are chosen at random, the chance that both are statistics books is

A) 10/21 B) 1/11 C) 1/21 D) 10/11

1.10 What is the median of the following set of values? 2, 16, 14, 10, 14, 9, 10, 14

A) 12 B) 10 C) 14 D) 8

1.8 What is the midrange of the following data set? 5, 11, 10, 12, 4, 12, 18, 18, 18

A) 12 B) 18 C) 11 D) 5

3.11 If a menu has a choice of 5 appetizers, 3 main courses, and 3 desserts, how many dinners are possible if each includes one appetizer, one main course, and one dessert?

A) 14 B) 45 C) 30 D) 3

2.34 In the Happy Hilltop Health Home, 10% of the residents play shuffleboard, 35% of the residents play poker, and 15% of the residents garden. If 5% of the residents play poker and garden, find the probability that a resident plays poker, given that they also garden.

A) 14.3% B) 33.3% C) 5.9% D) 7.7%

1.9 What is the median of the following data set? 6, 9, 13, 14, 18

A) 16 B) 12 C) 13 D) 14

1.4 What is the mode of the following data set? 5, 19, 17, 13, 17, 15, 12

A) 17 B) 11 C) 13 D) 15

1.6 A data set has a median of 84, and six of the numbers in the data set are less than median. The data set contains a total of n numbers. If n is odd, and exactly one number in the data set is equal to 84, what is the value of n?

A) 17 B) 15 C) 13 D) 16

3.10 How many different ways can four people: Andy, Betty, Cindy, and Doug, sit in a row at the opera if Andy and Betty must sit together?

A) 18 B) 12 C) 24 D) 6

1.3 Find the mean for the following data set: 25 24 21 13 14 15

A) 18 B) 12 C) 4.9 D) 18.7

1.17 The average weight of adult male bison in a particular federal wildlife preserve is 1450 pounds with a standard deviation of 240 pounds. Find the weight of an adult bull whose z-score is 1.5.

A) 1810 lb B) 1450 lb C) 1690 lb D) 1090 lb

2.20 If one card is drawn from an ordinary deck of cards, what is the probability that the card will be an ace, a king of hearts, or a spade?

A) 19/52 B) 17/52 C) 9/26 D) 11/26

2.16 A section of an exam contains two multiple-choice questions, each with three answer choices (listed "A", "B", and "C"). Assuming the outcomes to be equally likely, find the probability (as a reduced fraction) that at least one answer is "A". [Hint: List all the outcomes of the sample space first.]

A) 2/3 B) 5/9 C) 7/9 D) 1/3

3.14 A student and a professor each choose a number between 1 and 9 (1 and 9 are both possible choices). What is the probability that the two choose the same number?

A) 2/81 B) 1/9 C) 2/9 D) 1/81

3.6 A business has seven locations to choose from and wishes to rank only the top three locations. How many different ways can this be done?

A) 210 B) 420 C) 5,040 D) 840

3.3 Each of 5 students wishes to buy a particular textbook, but only 2 textbooks are available. How could one express the number of ways those textbooks could be distributed among the students?

A) 2C5 B) 2P5 C) 5C2 D) 5P2

3.8 How many ways can a student select five questions from an exam containing 12 questions, if one of the five must be the last question?

A) 330 B) 95,040 C) 40,320 D) 7920

1.22 Determine the range for the following data set. 4, 7, 3, 16, 5, 22, 8

A) 4 B) 14 C) 19 D) 3

2.19 A single card is drawn from a deck. Find the probability of selecting a heart or a 8.

A) 4/13 B) 17/52 C) 2/13 D) 1/4

2.5 The average weekly earnings in dollars for various industries are listed below. Find the percentile rank of 683. 755, 683, 604, 706, 649, 729, 800, 547, 821, 851

A) 45th B) 40th C) 25th D) 35th

3.2 Evaluate the combination: 12C8

A) 479,001,600 B) 495 C) 96 D) 19,958,400

3.7 A furniture manufacturer offers bookcases in 5 different sizes and 3 different colors. If every color is available in every size, then the total number of different bookcases is

A) 5 B) 15 C) 30 D) 8

2.18At Wassamatta University, 59.3% of the student body are males. Choose one student at random. What is the probability that the student is female?

A) 59.3% B) -9.3% C) 50% D) 40.7%

3.5 Evaluate the following: 7P3.

A) 6 B) 35 C) 5,040 D) 210

2.6 How many possible outcomes would there be if three coins were tossed once?

A) 6 B) 8 C) 4 D) 2

1.11 Find the sample variance for the following data set: 25 20 19 15 31

A) 6.2 B) 38 C) 16 D) 30.4

3.4 If the letters A, B, C, D, E, and F are to be used in a five-letter code, how many different codes are possible if repetitions are not permitted?

A) 625 B) 7,776 C) 720 D) 1,296

1.15 Find the sample standard deviation for the following data set: 25 13 31 33 20

A) 66.8 B) 8.2 C) 7.3 D) 53.4

3.9 A certain system has two components. There are 6 different models of the first component and 11 different models of the second. Any first component can be paired with any second component. A salesman must select 2 of the first component and 3 of the second to take on a sales call. How many different sets of components can the salesman take?

A) 6C5* 11C5 B) 6P5* 11P5 C) 6C2*1C3 D) 6P2*11P3

1.2 Find the mean of the following data set? 10, 5, 8, 3, 14

A) 7.0 B) 5.0 C) 8.0 D) 9.0

1.12 Given that the mean of a set of data is 25 and the standard deviation is 3, what is the coefficient of variation?

A) 8.33 B) 833% C) 0.12 D) 12%

3.1 Evaluate the permutation: 10P8

A) 80 B) 45 C) 1,814,400 D) 3,628,800

1.5 A student has an average of 78 on seven chapter tests. If the student's scores on six of the tests are 72, 82, 84, 66, 68, and 89, what was the score on the remaining test?

A) 85 B) 96 C) 77 D) 78

1.1 Which of the following is the properly rounded mean for the given data? 7, 8, 13, 9, 10, 11

A) 9 B) 9.7 C) 9.67 D) 10

2.26 What is the correct relationship between events A and B: A: Laura participated in an out-of-town volleyball game at 11:00 AM last Friday. B: Laura met with her academic advisor on campus at 11:00 AM last Friday.

A) A and B are mutually exclusive. B) A and B are complementary. C) A and B are not mutually exclusive. D) If B is true, A is true.

2.27 What is the correct relationship between events A and B: A: Kathleen made an A on her Biology final exam. B: Kathleen did not make an A on the Biology final exam.

A) A and B are mutually exclusive. B) A and B are complementary. C) A and B are not mutually exclusive. D) If B is untrue, A is untrue.

2.24 What is the correct relationship between events A and B: A: Karl is college graduate. B: Karl is a high school graduate.

A) A and B are mutually exclusive. B) B is the complement of A. C) A and B are not mutually exclusive. D) If B is not true, A cannot be true.

1.13 The completion times for a certain marathon race was 3 hours with a standard deviation of 0.5 hours. What can you determine about these data by using Chebyshev's Inequality with K = 2?

A) At least 88.9% of the completion times are between 2 hours and 4 hours. B) At most 88.9% of the completion times are between 2 hours and 4 hours. C) At least 75% of the completion times are between 2 hours and 4 hours. D) No more than 75% of the completion times are between 2 hours and 4 hours.

1.20 The average resident of Metro City produces 570 pounds of solid waste each year, and the standard deviation is approximately 70 pounds. Use Chebyshev's theorem to find the weight range that contains at least 75% of all residents' annual garbage weights.

A) Between 500 and 640 pounds B) Between 430 and 710 pounds C) Between 290 and 850 pounds D) Between 360 and 780 pounds

1.16 Indicate which student has the higher z score. Art Major X = 46 X(bar) = 50.5 s = 5.2 Theater Major X = 70 X(bar) = 75.1 s = 7.3

A) Both students have the same score. B) Neither student received a positive score; therefore, the higher score cannot be determined. C) The theater major has a higher score than the art major. D) The art major has a higher score than the theater major.

1.21 The range of a data set is the difference between the highest value and the lowest value.

A) False B) True

1.23 The coefficient of variation for a data set is the mean divided by the standard deviation, expressed as a percentage.

A) False B) True

1.24 Chebyshev's theorem can be used to find the minimum percentage of the values in a data set that will fall within a certain distance of the mean.

A) False B) True

2.2 Indicate which student has the higher z score. Art Major X = 46 X(bar) = 50.5 s = 5.2 Theater Major X = 70 X(bar) = 75.1 s = 7.3

A) Neither student received a positive score; therefore, the higher score cannot be determined. B) The art major has a higher score than the theater major. C) Both students have the same score. D) The theater major has a higher score than the art major.

2.35 When two events are independent, the probability of both occurring is:

A) P(A and B) = P(A) + P(B) B) P(A and B) = P(A) P(B) C) P(A and B) = 1 - (P(A) + P(B)) D) P(A and B) = 1 - P(A) P(B)

1.25 The variance of a data set is the square root of the standard deviation.

A) True B) False

2.1 The percentile corresponding to a given data value X is computed by adding the 0.5 to number of values less than X then dividing by the total number of values in the data set.

A) True B) False

2.11 Tree diagrams are useful for

A) finding all possible outcomes in a probability experiment involving several steps. B) ordering outcomes from lowest to highest. C) showing that the outcome is the set of all possible sample spaces. D) illustrating the law of large numbers.

1.7 A data set contains three unique values. Which of the following must be true?

A) mean = median B) none of these C) median = midrange D) mean = median = midrange

2.4 What is the set of all possible outcomes of a probability experiment?

A) the sample space B) an outcome C) a Venn diagram D) events

2.9 Nanette must pass through three doors as she walks from her company's foyer to her office. Each of these doors may be locked or unlocked. Let B be the event that exactly two doors are in the same condition. List the outcomes of B. [Let "L" designate "locked" and U" designate "unlocked".]

A) {LLL, LLU, LUL, LUU, ULL, ULU, UUL, UUU} B) {LLU, LUL, ULL} C) {LLU, LUL, ULL, LUU, ULU, UUL} D) None of these.

2.8 Nanette must pass through three doors as she walks from her company's foyer to her office. Each of these doors may be locked or unlocked. Let A be the event that all three doors are in the same condition. List the outcomes of A. [Let "L" designate "locked" and U" designate "unlocked".]

A) {LLL} B) {LLL, UUU} C) {LLL, LLU, LUL, LUU, ULL, ULU, UUL, UUU} D) None of these.

2.7 Nanette must pass through three doors as she walks from her company's foyer to her office. Each of these doors may be locked or unlocked.

List the outcomes of the sample space. A) {LLL, LLU, LUL, LUU, ULL, ULU, UUL, UUU} B) {LLL, UUU} C) {LLU, LUL, ULL, UUL, ULL, LUU} D) None of these.