Deck 5: Elementary Probability Theory

Question 1

If the probability that an event will happen is 0.27, what is the probability that the event won't happen?

A)0.23
B)0.63
C)0.73
D)0.83
E)1.73

Answer 1

0.73

Question 2

John runs a computer software store. He counted 130 people who walked by his store in a day, 59 of whom came into the store. Of the 59, only 24 bought something in the store. Estimate the probability that a person who comes into the store will buy nothing. Round your answer to the nearest hundredth.

A)0.82
B)0.55
C)0.27
D)0.59
E)none of these choices

Answer 2

0.59

Question 3

A coin is to be tossed 1000 times. What is the probability that the 785th toss is heads?

A)0
B)1/4
C)1/2
D)3/4
E)1

Answer 3

1/2

Question 4

John runs a computer software store. He counted 124 people who walked by his store in a day, 54 of whom came into the store. Of the 54, only 22 bought something in the store. Estimate the probability that a person who walks into the store will buy something. Round your answer to the nearest hundredth.

A)0.61
B)0.41
C)0.18
D)0.44
E)none of these choices

Question 5

Are customers more loyal in the East or in the West? The following table is based on information from Trends in the United Sates, published by the food marketing Institute, Washington, D.C. The columns represent loyalty (in years) at a primary supermarket. The rows represent regions of the United States. $$\begin{array} { l c r r r r r r } &\text { Less Than } & 1-2 & 3-4 & 5-9 & 10-14 & 15 \text { or More } & \text { Row Total } \\&1 \text { Year } & \text { Years } & \text { Years } & \text { Years } & \text { Years } & \text { Years }\\\text { East } & 32 & 54 & 59 & 112 & 77 & 118 & 452 \\\text { Midwest } & 31 & 68 & 68 & 120 & 63 & 173 & 523 \\\text { South } & 53 & 92 & 93 & 158 & 106 & 158 & 660 \\\text { West } & 41 & 56 & 67 & 78 & 45 & 86 & 373 \\\text { Column Total } & 157 & 270 & 287 & 468 & 291 & 535 & 2008\end{array}$$ What is the probability that a customer chosen at random has been loyal 5 or more years given that he or she is from the Midwest? Round your answer to the nearest thousandth.

A)0.177
B)0.275
C)0.681
D)0.417
E)none of these choices

Question 6

You draw two cards from a standard deck of 52 cards and do not replace the first one before drawing the second. State whether the following statement is true or false. The outcomes for the two cards are independent.

A)true
B)false

Question 7

Wing Foot is a shoe franchise commonly found in shopping centers across the United States. Wing Foot knows that its stores will not show a profit unless they gross over $940,000 per year. Let A be the event that a new Wing Foot store grosses over $940,000 its first year. Let B be the event that a store grosses over $940,000 its second year. Wing Foot has an administrative policy of closing a new store if it does not show a profit in either of the first two years. Assume that the accounting office at Wing Foot provided the following information: 64% of all Wing Foot stores show a profit the first year; 73% of all Wing Foot store show a profit the second year (this includes stores that did not show a profit the first year); however, 84% of Wing Foot stores that showed a profit the first year also showed a profit the second year. Compute , if , and . Round your answer to the nearest hundredth. $$P ( A \text { and } B )$$ $$P ( A ) = 0.64$$ $$P ( B ) = 0.73$$ $$P ( B \mid A ) = 0.84$$

A)0.76
B)0.87
C)0.53
D)0.84
E)0.54

Question 8

John runs a computer software store. He counted 120 people who walked by his store in a day, 57 of whom came into the store. Of the 57, only 20 bought something in the store. Estimate the probability that a person who walks by the store will come in and buy something. Round your answer to the nearest hundredth.

A)0.17
B)0.35
C)0.11
D)0.64
E)none of these choices

Question 9

Diagnostic tests of medical conditions have several results. The rest result can be positive or negative. A positive test (+) indicates the patient has the condition. A negative test (-) indicates the patient does not have the condition. Remember, a positive test does not prove the patient has the condition. Additional medical work may be required. Consider a random sample of 122 patients, some of whom have a medical condition and some of whom do not. Results of a new diagnostic test for the condition are shown. Assume that the sample is representative of the entire population. For a person selected at random, find P(getting test result - or condition present). Round your answer to the nearest hundredth.
$$\begin{array} { l c c r } & \text { Condition Present } & \text { Condition Absent } & \text { Row Total } \\\text { Test Result } + & 97 & 25 & 122 \\\text { Test Result } - & 25 & 37 & 62 \\\text { Column Total } & 122 & 62 & 184\end{array}$$

A)0.86
B)0.40
C)0.14
D)0.20
E)none of these choices

Question 10

You draw two cards from a standard deck of 52 cards and replace the first one before drawing the second. Find the probability of drawing a 10 for the first card and a king for the second card. Round your answer to the nearest thousandth.

A)0.006
B)0.039
C)0.019
D)0.155
E)0.038

Question 11

Are customers more loyal in the East or in the West? The following table is based on information from Trends in the United Sates, published by the food marketing Institute, Washington, D.C. The columns represent loyalty (in years) at a primary supermarket. The rows represent regions of the United States. What is the probability that a customer chosen at random is from the West given that he or she has been loyal 1 to 2 years? Round your answer to the nearest thousandth.
$$\begin{array} { l c r r r r r r } &\text { Less Than } & 1-2 & 3-4 & 5-9 & 10-14 & 15 \text { or More } & \text { Row Total } \\&1 \text { Year } & \text { Years } & \text { Years } & \text { Years } & \text { Years } & \text { Years }\\\text { East } & 32 & 54 & 59 & 112 & 77 & 118 & 452 \\\text { Midwest } & 31 & 68 & 68 & 120 & 63 & 173 & 523 \\\text { South } & 53 & 92 & 93 & 158 & 106 & 158 & 660 \\\text { West } & 41 & 56 & 67 & 78 & 45 & 86 & 373 \\\text { Column Total } & 157 & 270 & 287 & 468 & 291 & 535 & 2008\end{array}$$

A)0.028
B)0.207
C)0.417
D)0.150
E)none of these choices

Question 12

You draw two cards from a standard deck of 52 cards and replace the first one before drawing the second. Find the probability of drawing a king and a 6 in either order. Round your answer to the nearest thousandth.

A)0.078
B)0.012
C)0.037
D)0.311
E)0.036

Question 13

Are customers more loyal in the East or in the West? The following table is based on information from Trends in the United Sates, published by the food marketing Institute, Washington, D.C. The columns represent loyalty (in years) at a primary supermarket. The rows represent regions of the United States. What is the probability that a customer chosen at random is from the South given that he or she has been loyal 15 or more years? Round your answer to the nearest thousandth.
$$\begin{array} { l c r r r r r r } &\text { Less Than } & 1-2 & 3-4 & 5-9 & 10-14 & 15 \text { or More } & \text { Row Total } \\&1 \text { Year } & \text { Years } & \text { Years } & \text { Years } & \text { Years } & \text { Years }\\\text { East } & 32 & 54 & 59 & 112 & 77 & 118 & 452 \\\text { Midwest } & 31 & 68 & 68 & 120 & 63 & 173 & 523 \\\text { South } & 53 & 92 & 93 & 158 & 106 & 158 & 660 \\\text { West } & 41 & 56 & 67 & 78 & 45 & 86 & 373 \\\text { Column Total } & 157 & 270 & 287 & 468 & 291 & 535 & 2008\end{array}$$

A)0.079
B)0.239
C)0.295
D)0.417
E)none of these choices

Question 14

Wing Foot is a shoe franchise commonly found in shopping centers across the United States. Wing Foot knows that its stores will not show a profit unless they gross over $940,000 per year. Let A be the event that a new Wing Foot store grosses over $940,000 its first year. Let B be the event that a store grosses over $940,000 its second year. Wing Foot has an administrative policy of closing a new store if it does not show a profit in either of the first two years. Assume that the accounting office at Wing Foot provided the following information: 56% of all Wing Foot stores show a profit the first year; 71% of all Wing Foot store show a profit the second year (this includes stores that did not show a profit the first year); however, 80% of Wing Foot stores that showed a profit the first year also showed a profit the second year. Compute , if and . $$P ( B \mid \mathbf { A } )$$ $P ( A ) = 0.56$ $$P ( B \mid \text { not } \mathrm { A } ) = 0.37$$

A)0.66
B)0.80
C)0.52
D)0.63
E)none of these choices

Question 15

Diagnostic tests of medical conditions have several results. The rest result can be positive or negative. A positive test (+) indicates the patient has the condition. A negative test (-) indicates the patient does not have the condition. Remember, a positive test does not prove the patient has the condition. Additional medical work may be required. Consider a random sample of 128 patients, some of whom have a medical condition and some of whom do not. Results of a new diagnostic test for the condition are shown. Assume that the sample is representative of the entire population. For a person selected at random, find P(getting test result + and condition present). Round your answer to the nearest hundredth.
$$\begin{array} { l c c r } & \text { Condition Present } & \text { Condition Absent } & \text { Row Total } \\\text { Test Result } + & 107 & 21 & 128 \\\text { Test Result } - & 21 & 45 & 66 \\\text { Column Total } & 128 & 66 & 194\end{array}$$

A)0.84
B)0.55
C)1.62
D)0.66
E)none of these choices

Question 16

Are customers more loyal in the East or in the West? The following table is based on information from Trends in the United Sates, published by the food marketing Institute, Washington, D.C. The columns represent loyalty (in years) at a primary supermarket. The rows represent regions of the United States. What is the probability that a customer chosen at random has been loyal from 5 to 9 years given that he or she is from the West? Round your answer to the nearest thousandth.
$$\begin{array} { l c r r r r r r } &\text { Less Than } & 1-2 & 3-4 & 5-9 & 10-14 & 15 \text { or More } & \text { Row Total } \\&1 \text { Year } & \text { Years } & \text { Years } & \text { Years } & \text { Years } & \text { Years }\\\text { East } & 32 & 54 & 59 & 112 & 77 & 118 & 452 \\\text { Midwest } & 31 & 68 & 68 & 120 & 63 & 173 & 523 \\\text { South } & 53 & 92 & 93 & 158 & 106 & 158 & 660 \\\text { West } & 41 & 56 & 67 & 78 & 45 & 86 & 373 \\\text { Column Total } & 157 & 270 & 287 & 468 & 291 & 535 & 2008\end{array}$$

A)0.209
B)0.039
C)0.797
D)0.417
E)none of these choices

Question 17

Are customers more loyal in the East or in the West? The following table is based on information from Trends in the United Sates, published by the food marketing Institute, Washington, D.C. The columns represent loyalty (in years) at a primary supermarket. The rows represent regions of the United States. What is the probability that a customer chosen at random has been loyal from 3 to 4 years? Round your answer to the nearest thousandth.
$$\begin{array} { l c r r r r r r } &\text { Less Than } & 1-2 & 3-4 & 5-9 & 10-14 & 15 \text { or More } & \text { Row Total } \\&1 \text { Year } & \text { Years } & \text { Years } & \text { Years } & \text { Years } & \text { Years }\\\text { East } & 32 & 54 & 59 & 112 & 77 & 118 & 452 \\\text { Midwest } & 31 & 68 & 68 & 120 & 63 & 173 & 523 \\\text { South } & 53 & 92 & 93 & 158 & 106 & 158 & 660 \\\text { West } & 41 & 56 & 67 & 78 & 45 & 86 & 373 \\\text { Column Total } & 157 & 270 & 287 & 468 & 291 & 535 & 2008\end{array}$$

A)0.206
B)0.167
C)0.286
D)0.143
E)none of these choices

Question 18

Diagnostic tests of medical conditions have several results. The rest result can be positive or negative. A positive test (+) indicates the patient has the condition. A negative test (-) indicates the patient does not have the condition. Remember, a positive test does not prove the patient has the condition. Additional medical work may be required. Consider a random sample of 131 patients, some of whom have a medical condition and some of whom do not. Results of a new diagnostic test for the condition are shown.4 Assume that the sample is representative of the entire population. For a person selected at random, find P(). Round your answer to the nearest hundredth.
$$\begin{array} { l c c r } & \text { Condition Present } & \text { Condition Absent } & \text { Row Total } \\\text { Test Result } + & 115&16&131 \\\text { Test Result } - & 16&60&76 \\\text { Column Total } & 131&76&207\\\end{array}$$ $$\text { Condition present|getting test result } +$$

A)0.12
B)0.56
C)0.79
D)0.88
E)none of these choices

Question 19

When do creative people get their good ideas? Assume that the survey of 965 inventors gives the following information: Assuming that the time interval includes the left limit and all the times up to but not including the right limit, estimate the probability that an inventor has a good idea during the time interval from 6 P.M. to midnight. Write your answer as a fraction in simplest form.
$$\begin{array}{l}\text { Time of Day When Good Ideas Occur }\\\begin{array} { l c } { \text { Time } } & \begin{array} { c } \text { Number of } \\\text { Inventors }\end{array} \\6 \text { A.M. } - 12 \text { noon } & 284 \\12 \text { noon } - 6 \text { P.M. } & 133 \\6 \text { P.M. } - 12 \text { midnight } & 325 \\12 \text { midnight } - 6 \text { A.M. } & 223\end{array}\end{array}$$

A) $\frac { 1 } { 2 }$
B) $\frac { 1 } { 4 }$
C) $\frac { 65 } { 193 }$
D) $\frac { 65 } { 128 }$
E)none of these choices

Question 20

John runs a computer software store. He counted 125 people who walked by his store in a day, 52 of whom came into the store. Of the 52, only 27 bought something in the store. Estimate the probability that a person who walks by the store will enter the store. Round your answer to the nearest hundredth.

A)0.63
B)0.20
C)0.42
D)0.22
E)none of these choices

Question 21

There are three nursing positions to be filled at Lilly Hospital. Position 1 is the day nursing supervisor, position 2 is the night nursing supervisor; and position 3 is the nursing coordinator position. There are 10 candidates qualified for 3 of the positions. Determine the number of different ways that 3 positions can be filled by these applicants.

A)720
B)120
C)10
D)30
E)none of these choices

Question 22

How many sequences contain exactly two heads when you flip a coin six times?

A)4
B)12
C)15
D)8
E)none of these choices

Question 23

Draw a tree diagram to display all the possible head-tail sequences that can occur when you flip a coin two times.

A)
B)
C)
D)
E)

Question 24

Assuming the outcomes are all equally likely, what is the probability that you will get exactly three heads when you toss a coin five times?

A)0.60
B)0.31
C)0.30
D)0.50
E)none of these choices

Question 25

The qualified applicant pool for three management trainee positions consists of seven men and six women. If the applicants are equally qualified and the trainee positions are selected by drawing the names at random so that all groups of three are equally likely, what is the probability that the trainee class will consist entirely of men? Round your answer to the nearest thousandth.

A)0.007
B)0.073
C)0.122
D)0.003
E)none of these choices

Question 26

Barbara is a research biologist for Green Carpet Lawns. She is studying the effects of fertilizer type, temperature at time of application, and water treatment after application. She has five fertilizer types, four temperature zones, and three water treatments to test. Determine the number of different lawn plots she needs in order to test each fertilizer type, temperature range, and water treatment configuration.

A)12
B)3
C)24
D)4
E)60

Question 27

Compute . $$C ( 7,3 )$$

A)210
B)35
C)840
D)21
E)none of these choices

Question 28

Wing Foot is a shoe franchise commonly found in shopping centers across the United States. Wing Foot knows that its stores will not show a profit unless they gross over $940,000 per year. Let A be the event that a new Wing Foot store grosses over $940,000 its first year. Let B be the event that a store grosses over $940,000 its second year. Wing Foot has an administrative policy of closing a new store if it does not show a profit in either of the first two years. Assume that the accounting office at Wing Foot provided the following information: 65% of all Wing Foot stores show a profit the first year; 71% of all Wing Foot store show a profit the second year (this includes stores that did not show a profit the first year); however, 84% of Wing Foot stores that showed a profit the first year also showed a profit the second year. Compute if , , and . Round your answer to the nearest hundredth. $$P ( A \text { or } B )$$ $$P ( A ) = 0.65$$ $$P ( B ) = 0.71$$ $$P ( B \mid A ) = 0.84$$

A)0.46
B)0.78
C)0.81
D)0.52
E)0.84

Question 29

The qualified applicant pool for two management trainee positions consists of four men and six women. How many different groups of trainees would consist entirely of men?

A)2
B)8
C)6
D)1
E)none of these choices

Question 30

Eight wires (all with different colors) need to be attached to a circuit board. A robotic device will attach the wires. The wires can be attached in any order, and the production manager wishes to determine which order would be fastest for the robot to use. Use the multiplication rule of counting to determine the number of possible sequences of assembly that must be tested.

A)40,320
B)64
C)8
D)36
E)none of these choices

Question 31

Compute . $$P ( 7,3 )$$

A)35
B)21
C)840
D)210
E)none of these choices

Question 32

There are 15 qualified applicants for 5 trainee positions in a fast-food management program. How many different groups of trainees can be selected?

A)360,360
B)15
C)3003
D)75
E)none of these choices

Question 33

The qualified applicant pool for three management trainee positions consists of four women and two men. How many different groups of applicants can be selected for the positions?

A)20
B)6
C)1
D)8
E)none of these choices