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Sample questions from chapters 15 & 16 Final Exam will be commulative. Use study guides for midterms for the rest of the chapters 1 - 4,13,14. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) If we roll a regular six - sided die twice, the probability that both rolls will land as even numbers is 1) A) 1 2 . B) 1 3 . C) 1 4 . D) 3 4 . E) None of the above Answer: C 2) If a fair coin is tossed twice, the probability that at least one of the tosses will come up heads is 2) A) 3 4 . B) 1 3 . C) 1 4 . D) 1 2 . E) None of the above Answer: A 3) If a fair coin is tossed twice, the probability of both tosses coming up the same is 3) A) 1 3 . B) 1 4 . C) 1 2 . D) 3 4 . E) None of the above Answer: C 1

Probability

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Page 1: Probability

Sample questions from chapters 15 & 16Final Exam will be commulative. Use study guides for midterms for the rest of the chapters1-4,13,14.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Solve the problem.1) If we roll a regular six-sided die twice, the probability that both rolls will land as even numbers is 1)

A) 12

.

B) 13

.

C) 14

.

D) 34

.

E) None of the aboveAnswer: C

2) If a fair coin is tossed twice, the probability that at least one of the tosses will come up heads is 2)

A) 34

.

B) 13

.

C) 14

.

D) 12

.

E) None of the aboveAnswer: A

3) If a fair coin is tossed twice, the probability of both tosses coming up the same is 3)

A) 13

.

B) 14

.

C) 12

.

D) 34

.

E) None of the aboveAnswer: C

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Page 2: Probability

4) If a fair coin is tossed three times, the probability of tossing three heads is 4)

A) 38

.

B) 12

.

C) 18

.

D) 14

.

E) None of the aboveAnswer: C

5) A person shoots ten consecutive free throws and the total number of successes is observed. Howmany different outcomes are there in the sample space?

5)

A) 11B) 102

C) 210D) 5E) None of the above

Answer: A

6) An honest coin is tossed ten times . The probability of tossing two heads and eight tails is 6)

A) 451024

.

B) 15

.

C) 5512

.

D) 1512

.

E) None of the aboveAnswer: A

7) An honest coin is tossed ten times. The probability that the number of heads is double the numberof tails is

7)

A) 12

.

B) 13

.

C) 0.

D) 23

.

E) None of the aboveAnswer: C

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Page 3: Probability

8) An honest coin is tossed ten times. The probability that the number of heads is triple the number oftails is

8)

A) 0.

B) 13

.

C) 23

.

D) 12

.

E) None of the aboveAnswer: A

A pair of honest dice is rolled, and the number on each die is noted.9) What is the probability of rolling a total of either 7 or 11? 9)

A) 118

B) 136

C) 16

D) 14

E) None of the aboveAnswer: E

Solve the problem.10) Two cards are drawn in order from a well shuffled deck of 52 cards. The probability that both cards

are hearts is given by10)

A) 1352

×1351

.

B) 1352

.

C) 1352

×1252

.

D) 1352

×1251

.

E) None of the aboveAnswer: D

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Page 4: Probability

11) Three cards are drawn in order from a well shuffled deck of 52 cards. The probability that all threecards are 9's is given by

11)

A) 452

×352

×252

.

B) 452

×451

×450

.

C) 452

3.

D) 452

×351

×250

.

E) None of the aboveAnswer: D

12) Three cards are drawn in order from a well shuffled deck of 52 cards. The probability that all threecards are clubs is given by

12)

A)3 × 13C1

52C3.

B)3 × 13P1

52P3.

C) 13C3

52C3.

D) 13P3

52P3.

E) None of the aboveAnswer: D

A computer password is made up of five characters. Each character can be a capital letter (A through Z) or a digit (0through 9).

13) How many passwords have three letters and two digits? 13)A) 263 × 102B) 26 × 25 × 24 × 10 × 9C) 10 × 263 × 102

D) 3 × 263 × 102E) None of the above

Answer: C

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Page 5: Probability

Tasmanian automobile licence plates consist of three capital letters (A through Z) followed by three digits (0 through 9).14) How many Tasmanian license plates start with the word ZOO? 14)

A) 10B) 1000C) 1D) 100E) None of the above

Answer: B

15) How many Tasmanian license plates have no repeated symbols (different letters and differentdigits)?

15)

A) 26C3 × 10C3

B) 26P3 × 10P3

C) 26P3D) (263 - 1) × (103 - 1)E) None of the above

Answer: B

Tasmanian automobile license plates consist of four capital letters (A through Z) followed by three digits (0 through 9).16) How many Tasmanian license plates end with '66'? 16)

A) 264 × 103 - 1B) 264 × 10C) 262 × 103

D) 264 × 103E) None of the above

Answer: B

17) How many Tasmanian license plates start with the word MATH? 17)A) 100B) 1C) 10D) 1000E) None of the above

Answer: D

18) How many Tasmanian license plates have no repeated symbols (different letters and differentdigits)?

18)

A) 26P4 × 10P3B) 257

C) (264 - 1) × (103 - 1)

D) 26C4 × 10C3E) None of the above

Answer: A

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Page 6: Probability

A computer password is made up of four characters. Each character can be a capital letter (A through Z), a lowercase letter(a through z) or a digit (0 through 9).

19) How many passwords have 2 letters (uppercase or lowercase) and 2 digits? 19)A) 2 × 522 × 102

B) 522 × 102C) 52 × 51 × 10 × 9D) 6 × 522 × 102E) None of the above

Answer: D

A French restaurant offers a menu consisting of 5 different appetizers, 3 different salads, 2 different soups, 7 differentmain courses, and 3 different desserts. The restaurant offers different combinations of "fixed price dinners" on differentdays of the week.

20) On Monday through Thursday, the "fixed price dinner" consists of a choice of appetizer, a soup, amain course, and a dessert. Assuming you don't pass on any of these, how many different "fixedprice dinners" are possible on these days?

20)

A) 210B) 70C) 17D) 42E) None of the above

Answer: A

Solve the problem.21) A music CD consists of 10 songs numbered 1 through 10. In how many ways can the 10 songs be

ordered by the random function on a CD player?21)

A) 1010

B) 10C10C) 10!D) 10E) None of the above

Answer: C

22) The Tasmanian House of Representatives has 435 members (235 Demublicans and 200Republicrats). A set of 3 leaders - a Speaker, a Whip, and a Secretary - must be selected. Howmany different sets of leaders can be selected if the leaders cannot all be of the same political party?

22)

A) 4353 - 2353 - 2003

B) 435P3 - 235P3 - 200P3

C) 435C3

235C3 · 200C3

D) 235P3 + 200P3E) None of the above

Answer: B

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Page 7: Probability

23) 100C100 = 23)A) 100!B) 100C) 1D) 0E) None of the above

Answer: C

24) 1000C500

1000C501= 24)

A) 500 B) 500501 C) 501 D) 1

500 E) 501500

Answer: E

25) Forty-three drivers start a race. Assuming all the drivers are equally skilled, how many top tenfinishes are possible?

25)

A) 33

B) 43C10C) 33!

D) 43P10E) None of the above

Answer: D

26) In the spinner shown below, the regions numbered 1 and 2 correspond to 90 angles. The regionnumbered 3 corresponds to a 100 angle and the region numbered 4 corresponds to a 60 angle.Find the probability that, when spun randomly, the spinner will land on the region numbered 5.

26)

A) 118

B) 116

C) 117

D) 19

E) None of the aboveAnswer: A

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Page 8: Probability

27) Consider the sample space S = {o1, o2, o3, o4}. Suppose you are given Pr(o1) = 0.35 and Pr(o2) =14

.

If o3 and o4 have the same probability, find Pr(o3).

27)

A) 0.4B) 0.3C) 0.1D) 0.2E) None of the above

Answer: D

Four basketball teams called A, B, C, and D are entered in a tournament. According to the odds makers, the probabilitythat team A will win the tournament is Pr(A) = 0.1, and the other three teams all have an equal probability of winning thetournament.

28) What is the probability that team A will not win the tournament? 28)A) 0.4B) 0.9C) 0.3D) cannot be determined from the information givenE) None of the above

Answer: B

Solve the problem.29) Suppose that the odds against winning the grand prize in the lottery are 80,000,000 to 1. What is

the probability if winning the lottery?29)

A) 179,999,999

B) 79,999,99980,000,000

C) 180,000,000

D) 180,000,001

E) None of the aboveAnswer: D

A pitching machine throws 70% strikes and 30% balls. Five pitches will be thrown by the machine.30) What is the probability that the machine will throw three balls and two strikes? 30)

A) 0.06615B) 0.01323C) 0.1323D) 0.2E) All of the above are random experiments.

Answer: C

8

Page 9: Probability

Solve the problem.31) A submarine sandwich shop offers 8 fixings - lettuce, tomatoes, mayonnaise, swiss cheese, colby

cheese, onions, peppers, and mushrooms - on its basic ham sandwich. How many different hamsubmarine sandwiches can be made? (A ham submarine sandwich can have anywhere from nofixings to all 8 fixings included).

31)

A) 16 B) 40,320 C) 64 D) 8 E) 256Answer: E

32) There are 1000 tickets sold in a raffle. If you have 4 of these tickets and 10 prizes are to be given,what is the probability that each of your tickets will win a prize?

32)

A) 10C41000

B) 10 × 41000

C) 10C4

1000C4

D) 410

×1

1000E) None of the above

Answer: C

Answer the question(s) based on the following situation: 150 students in a math class take the final exam. The scores onthe exam have an approximately normal distribution with center µ = 65 and standard deviation = 10.

33) Peter's score on the exam places him in the 16th percentile of the class. Peter's score on the exam isapproximately

33)

A) 45.B) 16.C) 55.D) 35.E) None of the above

Answer: C

34) The third quartile of the scores on the exam is approximately 34)A) 80 points.B) 67 points.C) 84 points.D) 72 points.E) None of the above

Answer: D

Answer the question(s) based on the following situation: 250 students in a math class take the final exam. The scores onthe exam have an approximately normal distribution with center µ = 75 and standard deviation = 10.

35) Assuming there were no outliers, the lowest score on the exam was around 35)A) 75.B) 10.C) 45.D) 0.E) None of the above

Answer: C

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Page 10: Probability

36) Approximately what percent of the students scored between 65 and 75 points? 36)A) 10%B) 34%C) 95%D) 68%E) None of the above

Answer: B

37) The third quartile of the scores on the exam is approximately 37)A) 94 points.B) 82 points.C) 77 points.D) 90 points.E) None of the above

Answer: B

38) Approximately how many students had test scores between 68.25 and 85? 38)A) 188B) 85C) 107D) 147E) None of the above

Answer: D

Answer the question(s) based on the following situation: As part of a study on the metabolism of athletes, 400 collegebasketball players are randomly chosen and their weights taken. The distribution of the weights is approximatelynormal. The average weight is 215 pounds and the standard deviation is 15 pounds.

39) Of the 400 players approximately how many weighed 200 pounds or less? 39)A) 336B) 64C) 32D) 100E) None of the above

Answer: B

40) Approximately how many players had weights between 215 and 225 pounds? 40)A) 50B) 25C) 100D) 20E) None of the above

Answer: C

10

Page 11: Probability

Answer the question(s) based on the following situation: As part of a study, 800 college football players are randomlychosen and their weights taken. The distribution of the weights is approximately normal. The average weight is 235pounds and the standard deviation is 25 pounds.

41) The first quartile of the weights was approximately 41)A) 235 pounds.B) 223 pounds.C) 200 pounds.D) 218 pounds.E) None of the above

Answer: D

Refer to the following normal curve, with center µ and standard deviation .

42) The standard deviation = 42)A) 30B) 15C) 60D) 10E) None of the above

Answer: B

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Page 12: Probability

Refer to the following normal curve, with center µ and standard deviation .

43) The standard deviation = 43)A) 24B) 48C) 6D) 12E) None of the above

Answer: D

44) A data value of 30 corresponds to a standardized value of 44)A) 1.B) 2.C) -2.D) -1.E) None of the above

Answer: C

Refer to a normal distribution described by the following figure. The mean is µ and the standard deviation is .

45) The standard deviation = 45)A) 2B) 8C) 10D) 4E) None of the above

Answer: B

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Page 13: Probability

46) If the standardized value of x is -1.25, then x = 46)A) 42.5.B) 62.5.C) 65.D) 51.25.E) None of the above

Answer: A

Refer to a normal distribution described by the following figure. The mean is µ and the standard deviation is .

47) The standard deviation = 47)A) 54B) 80C) 108D) 27E) None of the above

Answer: B

Refer to the following normal curve, with center µ and standard deviation .

48) The standard deviation = 48)A) 40B) 54C) 27D) 100E) None of the above

Answer: A

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Page 14: Probability

Answer the question(s) based on the following situation: Over the last 80 years records have been kept of the annualrainfall in the Tasmanian desert. The distribution of annual rainfall is approximately normal and has no outliers. Theminimum of 4.5 inches of rain occurred in 1952; the maximum of 11.7 inches of rain occurred in 1934.

49) The standard deviation of the rainfall distribution is approximately 49)A) 1.8 inches.B) 1.2 inches.C) 7.2 inches.D) 3.6 inches.E) None of the above

Answer: B

Answer the question(s) based on the following situation: For a population of 4000 students taking the SAT math exam,the scores on the exam have an approximately normal distribution with center µ = 610 and standard deviation = 60.

50) A score of 700 has an approximate standardized value of 50)A) 1.5.B) -1.C) -1.75.D) 2.E) None of the above

Answer: A

Solve the problem.51) The standard deviation of a normal distribution is = 20. What is the interquartile range for this

distribution?51)

A) 13.5B) 33.75C) 27D) 6.75E) None of the above

Answer: C

52) If µ is the center and is the standard deviation of a normal distribution, then which of thefollowing statements is true?

52)

A) µ must always be bigger than .B) must always be positive, µ can be positive or negative.C) µ must always be positive, can be positive or negative.D) µ and must always be positive numbers.E) None of the above

Answer: B

Answer the question based on the following situation:An honest coin is tossed 1600 times. The random variable X denotes the total number of heads that come up in the 1600tosses.

53) What are the chances that X is between 760 and 840? 53)A) approximately 34%B) approximately 95%C) approximately 68%D) approximately 81.5%E) None of the above

Answer: B

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Page 15: Probability

Answer the question(s) based on the following situation: A dishonest coin (landing heads 25

of the time) is tossed 1350

times. The random variable X denotes the total number of heads that come up in the 1350 tosses.54) The mean µ of this approximately normal distribution X is approximately 54)

A) 675.B) 23.2.C) 540.D) 810.E) None of the above

Answer: C

55) The standard deviation of this approximately normal distribution X is approximately 55)A) 20.B) 18.37.C) 18.D) 18.63.E) None of the above

Answer: C

56) If the standardized value of x is 1.75, then x = 56)A) 541.5.B) 706.5.C) 711.D) 571.5E) None of the above

Answer: D

Solve the problem.57) The difference in the standardized values of Q3 and Q1 is about 57)

A) 0.675. B) 1.35. C) 3. D) 0.5. E) 1.Answer: B

58) A normal distribution has µ = 80 inches and Q3 = 93.5 inches. The standardized value of 40 inchesis

58)

A) -1. B) -0.675. C) -3. D) -2. E) -0.5.Answer: D

15