MGF 1106Review 2Prof. Nicoli-Suco----------------------

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Solve the problem involving probabilities with independent events.1) A single die is rolled twice. Find the probability of getting a 1 the first time and a 4 the

second time.1)

Answer: 136

2) You are dealt one card from a 52 card deck. Then the card is replaced in the deck, the deckis shuffled, and you draw again. Find the probability of getting a picture card the first timeand a spade the second time.

2)

Answer: 352

3) A card is drawn from a 52-card deck and a fair coin is flipped. What is the probability ofgetting jack and heads?

3)

Answer: 126

Solve the problem.4) Numbered disks are placed in a box and one disk is selected at random. If there are 4 red

disks numbered 1 through 4, and 3 yellow disks numbered 5 through 7, find theprobability of selecting a disk numbered 3, given that a red disk is selected.

4)

Answer: 14

5) Numbered disks are placed in a box and one disk is selected at random. If there are 2 reddisks numbered 1 through 2, and 8 yellow disks numbered 3 through 10, find theprobability of selecting a red disk, given that an odd-numbered disk is selected.

5)

Answer: 15

6) If a single fair die is rolled, find the probability of a 5 given that the number rolled is odd. 6)

Answer: 13

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Solve the problem involving probabilities with independent events.7) A single die is rolled twice. Find the probability of getting a 4 the first time and a 3 the

second time.7)

Answer: 136

8) You are dealt one card from a 52 card deck. Then the card is replaced in the deck, the deckis shuffled, and you draw again. Find the probability of getting a picture card the first timeand a diamond the second time.

8)

Answer: 352

Find the indicated probability.9) Assume that two marbles are drawn without replacement from a box with 1 blue, 3 white,

2 green, and 2 red marbles. Find the probability that both marbles are red.9)

Answer: 128

Solve the problem that involves probabilities with events that are not mutually exclusive.10) Consider a political discussion group consisting of 7 Democrats, 9 Republicans, and 4

Independents. Suppose that two group members are randomly selected, in succession, toattend a political convention. Find the probability of selecting an Independent and then aDemocrat.

10)

Answer: 795

11) Consider a political discussion group consisting of 4 Democrats, 8 Republicans, and 3Independents. Suppose that two group members are randomly selected, in succession, toattend a political convention. Find the probability of selecting an Independent and then aDemocrat.

11)

Answer: 235

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Find the indicated probability.12) Assume that two marbles are drawn without replacement from a box with 1 blue, 3 white,

2 green, and 2 red marbles. Find the probability that one marble is green, and one marble isred.

12)

Answer: 17

Solve the problem that involves probabilities with events that are not mutually exclusive.13) An ice chest contains 3 cans of apple juice, 6 cans of grape juice, 9 cans of orange juice, and

5 cans of pineapple juice. Suppose that you reach into the container and randomly selectthree cans in succession. Find the probability of selecting no grape juice.

13)

Answer: 6801771

Find the probability.14) If 81% of scheduled flights actually take place and cancellations are independent events,

what is the probability that 3 separate flights will all take place?14)

Answer: 0.53

Solve the problem.15) Numbered disks are placed in a box and one disk is selected at random. If there are 5 red

disks numbered 1 through 5, and 2 yellow disks numbered 6 through 7, find theprobability of selecting a disk numbered 3, given that a red disk is selected.

15)

Answer: 15

Find the probability.16) If two cards are drawn with replacement from an ordinary deck, find the probability the

first card is a heart and the second is a diamond.16)

Answer: 116

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

In the following exercises, does the problem involve permutations or combinations? Explain your answer. It is notnecessary to solve the problem.

17) A record club offers a choice of 7 records from a list of 45. In how many ways can a member makea selection?

17)

A) Permutations, because the order of the records selected does matter.B) Combinations, because the order of the records selected does not matter.

Answer: B

18) One hundred people purchase lottery tickets. Three winning tickets will be selected at random. Iffirst prize is $100, second prize is $50, and third prize is $25, in how many different ways can theprizes be awarded?

18)

A) Combinations, because the order of the prizes awarded does not matter.B) Permutations, because the order of the prizes awarded matters.

Answer: B

19) How many different user ID's can be formed from the letters W, X, Y, Z if no repetition of letters isallowed?

19)

A) Combinations, because the order of the letters does not matter.B) Permutations, because the order of the letters matters.

Answer: B

20) Five of a sample of 100 computers will be selected and tested. How many ways are there to makethis selection?

20)

A) Combinations, because the order of the computers selected does not matter.B) Permutations, because the order of the computers selected does matter.

Answer: A

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SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Given a group of students: G = {Allen, Brenda, Chad, Dorothy, Eric} or G = {A, B, C, D, E}, count the different ways ofchoosing the following officers or representatives for student congress. Assume that no one can hold more than oneoffice.

21) Three representatives, if two must be male and one must be female 21)Answer: 12

Solve the problem by applying the Fundamental Counting Principle with two groups of items.22) A restaurant offers 11 entrees and 10 desserts. In how many ways can a person order a

two-course meal?22)

Answer: 110

23) In how many ways can a girl choose a two-piece outfit from 5 blouses and 9 skirts? 23)Answer: 45

24) A restaurant offers a choice of 5 salads, 6 main courses, and 3 desserts. How many possible3-course meals are there?

24)

Answer: 90

25) There are 5 roads leading from Bluffton to Hardeeville, 10 roads leading from Hardeevilleto Savannah, and 4 roads leading from Savannah to Macon. How many ways are there toget from Bluffton to Macon?

25)

Answer: 200

26) An apartment complex offers apartments with four different options, designated by Athrough D.

A = number of bedrooms (one through four)B = number of bathrooms (one through three)C = floor (first through fifth)D = outdoor additions (balcony or no balcony)

How many apartment options are available?

26)

Answer: 120

27) A person can order a new car with a choice of 12 possible colors, with or without airconditioning, with or without heated seats, with or without anti-lock brakes, with orwithout power windows, and with or without a CD player. In how many different wayscan a new car be ordered in terms of these options?

27)

Answer: 384

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28) You are taking a multiple-choice test that has 6 questions. Each of the questions has 5choices, with one correct choice per question. If you select one of these options perquestion and leave nothing blank, in how many ways can you answer the questions?

28)

Answer: 15,625

29) License plates in a particular state display 2 letters followed by 3 numbers. How manydifferent license plates can be manufactured? (Repetitions are allowed.)

29)

Answer: 676,000

Use the theoretical probability formula to solve the problem. Express the probability as a fraction reduced to lowestterms.

30) A die is rolled. The set of equally likely outcomes is {1, 2, 3, 4, 5, 6}. Find the probability ofgetting a 7.

30)

Answer: 0

Given a group of students: G = {Allen, Brenda, Chad, Dorothy, Eric} or G = {A, B, C, D, E}, count the different ways ofchoosing the following officers or representatives for student congress. Assume that no one can hold more than oneoffice.

31) A treasurer and a secretary if the two must not be the same sex 31)Answer: 12

Use the theoretical probability formula to solve the problem. Express the probability as a fraction reduced to lowestterms.

32) A die is rolled. The set of equally likely outcomes is {1, 2, 3, 4, 5, 6}. Find the probability ofgetting a 3.

32)

Answer: 16

33) You are dealt one card from a standard 52-card deck. Find the probability of being dealt apicture card.

33)

Answer: 313

34) You are dealt one card from a standard 52-card deck. Find the probability of being dealtan ace or a 7.

34)

Answer: 213

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Solve the problem.35) In how many distinct ways can the letters in MANAGEMENT be arranged? 35)

Answer: 226,800

Use the Fundamental Counting Principle to solve the problem.36) There are 5 performers who are to present their acts at a variety show. How many

different ways are there to schedule their appearances?36)

Answer: 120

37) There are 5 performers who are to present their acts at a variety show. One of them insistson being the first act of the evening. If this request is granted, how many different ways arethere to schedule the appearances?

37)

Answer: 24

Four accounting majors, two economics majors, and three marketing majors have interviewed for five different positionswith a large company. Find the number of different ways that five of these could be hired.

38) There is no restriction on the college majors hired for the five positions. 38)Answer: 15,120 ways

Use the empirical probability formula to solve the exercise. Express the answer as a fraction. Then express the probabilityas a decimal, rounded to the nearest thousandth, if necessary.

39) The table below represents a random sample of the number of deaths per 100 cases for acertain illness over time. If a person infected with this illness is randomly selected from allinfected people, find the probability that the person lives 3-4 years after diagnosis.Years after Diagnosis Number deaths1-2 153-4 355-6 167-8 99-10 611-12 413-14 215+ 13

39)

Answer: 35100

; 0.35

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The chart below shows the percentage of people in a questionnaire who bought or leased the listed car models and werevery satisfied with the experience.

Model A 81%Model B 79%Model C 73%Model D 61%Model E 59%Model F 57%

40) With which model was the greatest percentage satisfied? Estimate the empiricalprobability that a person with this model is very satisfied with the experience. Express theanswer as a fraction with a denominator of 100.

40)

Answer: Model A; 81100

41) The empirical probability that a person with a model shown is very satisfied with the

experience is 79100

. What is the model?

41)

Answer: B

You are dealt one card from a 52-card deck. Find the probability that you are not dealt:42) a 6. 42)

Answer: 1213

Of the 2,598,960 different five-card hands possible from a deck of 52 playing cards, how many would contain thefollowing cards?

43) Two red cards and three black cards 43)Answer: 845,000 hands

You are dealt one card from a 52-card deck. Find the probability that you are not dealt:44) a spade. 44)

Answer: 34

Solve the problem.45) A bag contains 5 apples and 3 oranges. If you select 4 pieces of fruit without looking, how

many ways can you get 4 oranges?45)

Answer: 0 ways

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Solve the problem involving probabilities with independent events.46) A spinner is used for which it is equally probable that the pointer will land on any one of

six regions. Three of the regions are colored red, two are colored green, and one is coloredyellow. If the pointer is spun once, find the probability it will land on green and thenyellow.

46)

Answer: 118

Solve the problem.47) If a license plate consists of two letters followed by four digits, how many different licenses

could be created having at least one letter or digit repeated.47)

Answer: 3,484,000 licenses

A bag contains 6 cherry, 3 orange, and 2 lemon candies. You reach in and take 3 pieces of candy at random. Find theprobability.

48) 2 orange, 1 lemon 48)Answer: 0.0364

49) All cherry 49)Answer: 0.1212

Solve the problem.50) A ring contains 8 keys: 1 red, 1 blue, and 6 gold. If the keys are arranged at random on the

ring, find the probability that the red is next to the blue.50)

Answer: 0.286

Find the requested probability.51) A family has five children. The probability of having a girl is 1/2. What is the probability of

having exactly 2 girls and 3 boys?51)

Answer: 0.3125

52) A family has five children. The probability of having a girl is 1/2. What is the probability ofhaving no girls?

52)

Answer: 0.0313

A die is rolled five times and the number of fours that come up is tallied. Find the probability of getting the given result.53) Exactly zero fours 53)

Answer: 0.402

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Find the requested probability.54) A fair coin is tossed 5 times. What is the probability of no heads? 54)

Answer: 0.0313

Solve.55) In a state lotto you have to pick 4 numbers from 1 to 46. If your numbers match those that

the state draws, you win. If you buy 3 tickets, what is your probability of winning?55)

Answer: 154395

Find the requested probability.56) A child rolls a 6-sided die 6 times. What is the probability of the child rolling exactly four

fives?56)

Answer: 0.0080

A bag contains 6 cherry, 3 orange, and 2 lemon candies. You reach in and take 3 pieces of candy at random. Find theprobability.

57) All lemon 57)Answer: 0

58) 2 cherry, 1 lemon 58)Answer: 0.1818

59) One of each flavor 59)Answer: 0.2182

Solve.60) A lottery game contains 26 balls numbered 1 through 26. What is the probability of

choosing a ball numbered 27?60)

Answer: 0

61) In a state lotto you have to pick 4 numbers from 1 to 42. If your numbers match those thatthe state draws, you win. If you buy 3 tickets, what is your probability of winning?

61)

Answer: 137310

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Solve the problem.62) At the first tri-city meeting, there were 8 people from town A, 7 people from town B, and 5

people from town C. If the council consists of 5 people, find the probability of 3 from townA and 2 from town B.

62)

Answer: 0.076

63) At the first tri-city meeting, there were 8 people from town A, 7 people from town B, and 5people from town C. If the council consists of 5 people, find the probability of 2 from townA, 2 from town B, and 1 from town C.

63)

Answer: 0.189

64) Suppose 6 people sit at a circular table. Find the probability that 2 particular people aresitting next to each other.

64)

Answer: 0.4

65) A ring contains 8 keys: 1 red, 1 blue, and 6 gold. If the keys are arranged at random on thering, find the probability that the red is next to the blue.

65)

Answer: 0.286

Find the requested probability.66) A family has five children. The probability of having a girl is 1/2. What is the probability of

having exactly 3 girls and 2 boys?66)

Answer: 0.3125

67) A family has five children. The probability of having a girl is 1/2. What is the probability ofhaving at least 4 girls?

67)

Answer: 0.1875

A die is rolled five times and the number of fours that come up is tallied. Find the probability of getting the given result.68) Exactly zero fours 68)

Answer: 0.402

69) Exactly one four 69)Answer: 0.402

70) Exactly two fours 70)Answer: 0.161

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71) Exactly three fours 71)Answer: 0.032

A die is rolled 20 times and the number of twos that come up is tallied. Find the probability of getting the given result.72) Exactly four twos 72)

Answer: 0.202

73) Exactly two twos 73)Answer: 0.198

Find the requested probability.74) A child rolls a 6-sided die 6 times. What is the probability of the child rolling exactly four

fives?74)

Answer: 0.0080

75) A fair coin is tossed 5 times. What is the probability of no heads? 75)Answer: 0.0313

76) A fair coin is tossed 5 times. What is the probability of exactly 4 heads? 76)Answer: 0.1563

77) What is the probability that 20 tosses of a fair coin will show 12 tails? 77)Answer: 0.1201

In a certain college, 33% of the physics majors belong to ethnic minorities. Find the probability of the event from arandom sample of 10 students who are physics majors.

78) Exactly 2 belong to an ethnic minority. 78)Answer: 0.1990

79) Exactly 4 do not belong to an ethnic minority. 79)Answer: 0.0547

80) No more than 6 belong to an ethnic minority. 80)Answer: 0.9815

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Find the probability of the event.81) A die is rolled 18 times and two threes come up. 81)

Answer: 0.230

82) A 10-question multiple choice test has 4 possible answers for each question. A studentselects at least 6 correct answers.

82)

Answer: 0.020

83) The probability that a radish seed will germinate is 0.7. The gardener plants 20 seeds andshe harvests 16 radishes.

83)

Answer: 0.130

84) On a hospital floor, 16 patients have a disease with a mortality rate of 0.1. Two of them die. 84)Answer: 0.275

85) A battery company has found that the defective rate of its batteries is 0.03. Each day, 22batteries are randomly tested. On Tuesday, 1 is found to be defective.

85)

Answer: 0.348

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