Deck 7: Probability

Question 1

An experiment consists of tossing a coin, rolling a die, and observing the outcomes. Describe an appropriate sample space for this experiment.

A) {(H, H, H, H, H, H, T, T, T, T, T, T, 1, 2, 3, 4, 5, 6)}
B) {(1, 2, 3, 4, 5, 6), (H, T)}
C) {(H, 1), (T, 2), (H, 3), (T, 4), (H, 5), (T, 6), (T, 1), (T, 4), (T, 5), (H, 6)}
D) {(1, H, T), (2, H, T), (3, H, T), (4, H, T), (5, H, T), (6, H, T)}
E) {(H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6), (T, 1), (T, 2), (T, 3), (T, 4), (T, 5), (T, 6)}

Answer 1

{(H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6), (T, 1), (T, 2), (T, 3), (T, 4), (T, 5), (T, 6)}

Question 2

In a television game show, the winner is asked to select three prizes from five different prizes, A, B, C, D, and E. Describing a sample space of possible outcomes (order is not important) determine the number of points there are in the sample space corresponding to a selection that includes A.

A) 6
B) 9
C) 4
D) 2

Answer 2

6

Question 3

A sample of two transistors taken from a local electronics store was examined to determine whether the transistors were defective (d) or nondefective (n). What is an appropriate sample space for this experiment? ​

A) {dd, dn, nd}
B) {dd, dn, nd, nn}
C) {dd, nn, nd}
D) {(d,d), (n,n)}

Answer 3

{dd, dn, nd, nn}

Question 4

Let be a sample space of an experiment and let be events of this experiment. ​
Find the events F^c and E ∩ Gc.

A)
B)
C)
D)

Question 5

An experiment consists of selecting a card from a standard deck of playing cards and noting whether the card is black (B) or red (R). Describe an appropriate sample space for this experiment. ​

A) {BR, RB}
B) {R, R}
C) {R, B, B, R}
D) {B, R}
E) {B, B}

Question 6

Let be a sample space of an experiment with outcomes p, q and r. List all the events of this experiment. ​

A) Ø, {p}, {q}, {r}, {p, q}, {p, r}, {q, r}, S
B) {p}, {q}, {r}
C) Ø, {p}, {q}, {r}, {p, q}, {p, r}, {q, r}
D) {p}, {q}, {r}, {p, q}, {p, r}, {q, r}

Question 7

An experiment consists of casting a pair of dice and observing the number that falls uppermost on each die. We may represent each outcome of the experiment by an ordered pair of numbers, the first representing the number that appears uppermost on the first die and the second representing the number that appears uppermost on the second die. Consider the sample space S = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6),
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}
Determine the event that the number that falls uppermost on the second die is double that of the number that falls on the first die.

A) {(1, 2), (2, 4), (3, 6)}
B) {(3, 1), (2, 6), (4, 4)}
C) {(1, 1), (2, 1), (1, 6)}
D) {(1, 2), (5, 3), (6, 6)}

Question 8

An experiment consists of casting a pair of dice and observing the number that falls uppermost on each die. We may represent each outcome of the experiment by an ordered pair of numbers, the first representing the number that appears uppermost on the first die and the second representing the number that appears uppermost on the second die. Consider the sample space S = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6),
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}
Determine the event that the number that falls uppermost on the first die is greater than the number that falls uppermost on the second die.

A) {(2, 1), (3, 1), (4, 1), (5, 1), (6, 1), (3, 2), (4, 2), (5, 2), (6, 2), (4, 3), (5, 3), (6, 3), (5, 4), (6, 4), (6, 5)}
B) {(1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (3, 2), (4, 2), (5, 2), (6, 2), (4, 3), (5, 3), (6, 3), (5, 4), (6, 4), (5, 6)}
C) {(2, 1), (3, 1), (4, 1), (5, 1), (6, 1), (2, 3), (2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6), (4, 5), (6, 4), (6, 5)}
D) Ø

Question 9

Let S = {1, 2, 3, 4, 5, 6}, E = {1, 3, 5}, F = {2, 4, 6} and G = {2, 3}. Are the events F and G mutually exclusive?

A) yes
B) no

Question 10

Let be a sample space of an experiment and let , and be events of this experiment. ​
Find the events E ∪ F and E ∩ F.
​

A)
B)
C)
D)

Question 11

An experiment consists of casting a pair of dice and observing the number that falls uppermost on each die. We may represent each outcome of the experiment by an ordered pair of numbers, the first representing the number that appears uppermost on the first die and the second representing the number that appears uppermost on the second die. Consider the sample space S = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6),
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}
Determine the event that the number falling uppermost on one die is a 4 and the number falling uppermost on the other die is less than 4.

A) {(1, 4), (2, 4), (3, 4), (4, 3), (4, 2), (4, 1)}
B) {(4, 5), (4, 6), (5, 2), (6, 4)}
C) {(2, 3), (2, 4), (6, 5), (2, 6), (3, 2), (4, 2), (5, 1), (6, 2)}
D) Ø

Question 12

An experiment consists of tossing a coin, rolling a die, and observing the outcomes. Describe the event "A head is tossed and an even number is rolled."

A)
B)
C)
D)

Question 13

An experiment consists of casting a pair of dice and observing the number that falls uppermost on each die. We may represent each outcome of the experiment by an ordered pair of numbers, the first representing the number that appears uppermost on the first die and the second representing the number that appears uppermost on the second die. Consider the sample space S = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6),
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}
Determine the event that the sum of the numbers falling uppermost is greater than or equal to 7.

A) {(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)}
B) {(1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 3), (2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6), (4, 5), (4, 6), (5, 6)}
C) {(1, 6), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6), (4, 3), (4, 5), (4, 6), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}
D) Ø

Question 14

An experiment consists of selecting a card from a standard deck of playing cards and noting whether the card is black (B) or red (R). What are the events of this experiment? ​

A) {B, R}, {R, B}
B) {Ø}, {B}, {R}
C) {B}, {R}, {B, B}, {R, R}
D) {Ø}, {B}, {R}, {B, R}
E) {Ø}, {B, R}, {R, B}, {R, R}, {B, B}

Question 15

Let S = {1, 2, 3, 4, 5, 6}, E = {1, 3, 5}, F = {2, 4, 6} and G = {3, 4}. Are the events F and G complementary?

A) no
B) yes

Question 16

A die is cast and the number that falls uppermost is observed. Let E denote the event that the number shown is a 6 and let F denote the event that the number shown is an even number. ​
Are the events E and F mutually exclusive?

A) no
B) yes

Question 17

Let S = {1, 2, 3, 4, 5, 6}, E = {1, 3, 5}, F = {2, 4, 6} and G = {2, 3} . Find the event E ∪ F ∪ G.

A) E ∪ F ∪ G = {2, 3, 4, 5, 7}
B) E ∪ F ∪ G = {1, 3, 4, 5, 6}
C) E ∪ F ∪ G = {1, 2, 3, 4, 5, 6}
D) E ∪ F ∪ G = {1, 2, 3, 5, 6}

Question 18

An experiment consists of selecting a letter at random from the letters in the word PENNSYLVANIA and observing the outcomes. What is an appropriate sample space for this experiment? ​

A)
B)
C)
D)

Question 19

Let be a sample space of an experiment and let be events of this experiment. ​
Are the events E and F mutually exclusive?

A) yes
B) no

Question 20

Let S = {1, 2, 3, 4, 5, 6}, E = {2, 4, 6, }, F = {1, 3, 5} and G = {4, 5} . ​
Find the event (E ∩ F ∩ G)c.
​

A) (E ∩ F ∩ G)c = {1, 2, 3, 4, 5, 6}
B) (E ∩ F ∩ G)c = {1, 2, 3, 4, 5}
C) (E ∩ F ∩ G)c = {2, 3, 4, 5, 6}
D) (E ∩ F ∩ G)c = {1, 2, 5, 6, 9}

Question 21

Let S be a sample space for an experiment and let G and A be events of this experiment. Show that the events and are mutually exclusive. ​
Hint: Use De Morgan's law.
​

A) By De Morgan's law, , so the events are mutually exclusive.
B) By De Morgan's law, , so the events are mutually exclusive.
C) By De Morgan's law, , so the events are mutually exclusive.
D) By De Morgan's law, , so the events are mutually exclusive.
E) By De Morgan's law, , so the events are not mutually exclusive.

Question 22

Let S be any sample space and N, F, and E be any three events associated with the experiment. Describe the following event, using the symbols ∪, ∩, and ^c. ​
The event that E does not occur.
​

A) E^c
B)
C)
D)
E)

Question 23

A certain airport hotel operates a shuttle bus service between the hotel and the airport. The maximum capacity of a bus is 20 passengers. On alternate trips of the shuttle bus over a period of 1 wk, the hotel manager kept a record of the number of passengers arriving at the hotel in each bus. Describe the event E that a shuttle bus carried fewer than twelve passengers.

A) {0, 1, 2, 3, 4, 5, 6, 7, 8}
B) {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}
C) {0, 1, 2, 3, 4, 5, 6, 7}
D) {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}

Question 24

An experiment consists of casting a pair of dice and observing the number that falls uppermost on each die. We may represent each outcome of the experiment by an ordered pair of numbers, the first representing the number that appears uppermost on the first die and the second representing the number that appears uppermost on the second die. Consider the sample space
S = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6),
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}
Determine the event that the sum of the numbers falling uppermost is less than or equal to 6.
Express your answer using set notation.

Question 25

As part of a quality-control procedure, an inspector at Bristol Farms randomly selects ten eggs from each consignment of eggs he receives and records the number of broken eggs. Describe the event F that at least nine eggs are broken.

A) {9, 10}
B) {7, 8, 9, 10}
C) {6, 7, 8, 9, 10}
D) {0, 1, 2, 3, 4, 5}

Question 26

Eight players, A, B, C, D, E, F, G, and H, are competing in a series of elimination matches of a tennis tournament in which the winner of each preliminary match will advance to the semifinals and the winner of the semifinals will advance to the finals. An outline of the scheduled matches follows. Describe a sample space listing the possible participants in the finals.

A) S = {(A,D), (A,F), (A,H), (C,B), (C,F), (C,H), (E,B), (E,D), (E, H), (G,B),
(G,D), (G,F)}
B) S = {(A,B), (A,D), (A,F), (A,H), (C,B), (C,D), (C,F), (C,H), (E,B), (E,D),
(E,F), (E, H), (G,B), (G,D), (G,F), (G,H)}
C) S = {(A,E), (A,F), (A,G), (A,H), (B,E), (B,F), (B,G), (B,H), (C, E), (C,F),
(C,G), (C,H), (D,E), (D,F), (D,G), (D,H)}
D) S = {(A,B), (A,C), (A,D), (B,С), (B,D), (C,D), (E,F), (E,G), (E, H), (F,G),
(F,H), (G,H)}
E) None of the above.

Question 27

The customer service department of Universal Instruments, manufacturer of the Galaxy home computer, conducted a survey among customers who had returned their purchase registration cards. Purchasers of its deluxe model home computer were asked to report the length of time (t) in days before service was required. Describe a sample space corresponding to this survey.

A) {t | t > 0}
B) {t | 0 < t ≤ 370}
C) {t | 100 ≤ t ≤ 370}
D) {t | 0 < t ≤ 100}

Question 28

An experiment consists of casting a pair of dice and observing the number that falls uppermost on each die. We may represent each outcome of the experiment by an ordered pair of numbers, the first representing the number that appears uppermost on the first die and the second representing the number that appears uppermost on the second die. Consider the sample space
S = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6),
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}
Determine the event that the number that falls uppermost on the first die is less than the number that falls uppermost on the second die.
Express your answer using set notation.

Question 29

An experiment consists of casting a pair of dice and observing the number that falls uppermost on each die. We may represent each outcome of the experiment by an ordered pair of numbers, the first representing the number that appears uppermost on the first die and the second representing the number that appears uppermost on the second die. Consider the sample space
S = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6),
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}
Determine the event that the number that falls uppermost on the second die is double that of the number that falls on the first die.
Express your answer using set notation.

Question 30

Let be a sample space of an experiment with outcomes k, l and m. List all the events of this experiment.
​
Express your answer using set notation.

Question 31

Let , , and .
Find the event E ∪ F ∪ G.
Express your answer using set notation.

Question 32

Robin purchased shares of a machine tool company and shares of an airline company. Let E be the event that the shares of the machine tool company increase in value over the next 5 months, and let F be the event that the shares of the airline company increase in value over the next 5 months. Using the symbols ∪, ∩ and ^c describe the event that the shares of only one of the two companies increase in value.

A) (E ∩ F^c) ∪ (E^c ∩ F)
B) E ∪ F
C) E^c ∩ F^c
D) Ø

Question 33

Human blood is classified by the presence or absence of three main antigens (A, B, and Rh). When a blood specimen is typed, the presence of the A and/or B antigen is indicated by listing the letter A and/or the letter B. If neither the A nor B antigen is present, the letter O is used. The presence or absence of the Rh antigen is indicated by the symbols + or -, respectively. Thus, if a blood specimen is classified as AB⁺, it contains the A and the B antigens as well as the Rh antigen. Similarly, O^- blood contains none of the three antigens. Using this information, determine the sample space corresponding to the different blood groups.

A) {AB⁺, AB^-, AO⁺, BO⁺, AO^-, BO^-, O⁺, O^-}
B) {AB⁺, AB^-, O⁺, O^-}
C) {A⁺, B⁺, A^-, B^-, O⁺, O^-}
D) {AB⁺, AB^-, A⁺, B⁺, A^-, B^-, O⁺, O^-, ABO^-, AO⁺, AO^-, BO⁺, BO^-}
E) {AB⁺, AB^-, A⁺, B⁺, A^-, B^-, O⁺, O^-}

Question 34

Let S be any sample space and K, E, and M be any three events associated with the experiment. Describe the following event, using the symbols ∪, ∩, and ^c.
​
The event that M does not occur.

Question 35

An experiment consists of casting a pair of dice and observing the number that falls uppermost on each die. We may represent each outcome of the experiment by an ordered pair of numbers, the first representing the number that appears uppermost on the first die and the second representing the number that appears uppermost on the second die. Consider the sample space
S = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6),
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}
Determine the event that the number falling uppermost on one die is a 2 and the number falling uppermost on the other die is greater than 2.
Express your answer using set notation.

Question 36

Let , , and .
​
Find the event .
​
Express your answer using set notation.

Question 37

An experiment consists of selecting a letter at random from the letters in the word LOUISIANA and observing the outcomes. What is an appropriate sample space for this experiment?
​
Express your answer using set notation.

Question 38

An opinion poll is conducted among a state's electorate to determine the relationship between their income levels and their stands on a proposition aimed at reducing state income taxes. Voters are classified as belonging to either the low-, middle-, or upper-income group. They are asked whether they favor, oppose, or are undecided about the proposition. Let the letters L, M, and U represent the low-, middle-, and upper-income groups, respectively, and let the letters f, o, and u represent the responses - favor, oppose, and undecided, respectively. ​
Describe the event E that a respondent does not oppose the proposition and does not belong to the upper-income group.
​

A) E = {(L,o), (L,u), (L,f), (M,o), (M,u), (M,f), (U,o), (U,u)}
B) E = {(L,f), (L,u), (M,f), (M,u)}
C) E = {(L,f), (M,f), (U,o), (U,u)}
D) E = {(L,o), (L,u), (L,f), (M,o), (M,u), (M,f)}
E) E = {(L,o), (L,u), (M,o), (M,u), (U,f)}

Question 39

Let be a sample space associated with an experiment. How many subsets of S contain either the number 2 or the number 1?

A) 5
B) 7
C) 4
D) 6
E) 3

Question 40

A time study was conducted by the production manager of Vista Vision to determine the length of time (t) in minutes required by an assembly worker to complete a certain task during the assembly of its Pulsar color television sets. Describe a sample space corresponding to this time study.

A) {t | 0 < t < 8}
B) {t | 8 ≤ t ≤ 10}
C) {t | 0< t ≤ 10}
D) {t | t > 0}

Question 41

Eight players, A, B, C, D, E, F, G, and H, are competing in a series of elimination matches of a tennis tournament in which the winner of each preliminary match will advance to the semifinals and the winner of the semifinals will advance to the finals. An outline of the scheduled matches follows. Describe a sample space listing the possible participants in the finals.
​

Question 42

The grade distribution for a certain class is shown in the table. Find the probability distribution associated with these data. ​

A) ​ ​
B) ​
C) ​
D) ​ ​

Question 43

Let be a sample space of an experiment and let , and be events of this experiment.
​
Are the events E and F mutually exclusive? Answer yes or no.

Question 44

If a ball is selected at random from an urn containing two red balls, three white balls, and five blue balls, what is the probability that it will be a white ball?

A) The probability is 0.31
B) The probability is 0.33
C) The probability is 0.30
D) The probability is 0.32

Question 45

In a survey of 3000 adults 18 year old and older conducted in 2000, the following question was asked : Is your family income keeping pace with the cost of living ? The results of the survey follow : Determine the empirical probability distribution associated with these data.

A) ​
B) ​ ​
C) ​ ​
​
D) ​ ​

Question 46

The number of subscribers to five leading e-mail services is shown in the accompanying table: Find the empirical probability distribution associated with these data.

A) ​ ​
​
B) ​ ​
​
C) ​ ​
​
D) ​ ​
​

Question 47

The following breakdown of a total of 18,613 transportation fatalities that occured in 2007 was obtained from records compiled by the U.S. Department of Transportation (DOT). What is the probability that a victim randomly selected from this list of transportation fatalities for 2007 died in a car crash or bicycle accident? Round answer to two decimal places.

A) 0.98
B) 0.92
C) 0.89
D) 0.93

Question 48

One light bulb is selected at random from a lot of 140 light bulbs, of which 2% are defective. What is the probability that the light bulb selected is defective? ​

A) The probability is 0.04
B) The probability is 0.01
C) The probability is 0.02
D) The probability is 0.03

Question 49

In a poll conducted among 2,000 college freshmen to ascertain the political views of college students, the accompanying data were obtained: A: Far Left B: Liberal
C: Middle of the road
D: Conservative
E: Far right
Determine the empirical probability distribution associated with these data.

A) ​ ​
B) ​ ​
C) ​ ​
D) ​ ​

Question 50

Human blood is classified by the presence or absence of three main antigens (A, B, and Rh). When a blood specimen is typed, the presence of the A and/or B antigen is indicated by listing the letter A and/or the letter B. If neither the A nor B antigen is present, the letter O is used. The presence or absence of the Rh antigen is indicated by the symbols + or -, respectively. Thus, if a blood specimen is classified as AB⁺, it contains the A and the B antigens as well as the Rh antigen. Similarly, O- blood contains none of the three antigens.
​
Using this information, determine the sample space corresponding to the different blood groups.

Question 51

List the simple events associated with the given experiment. ​
As part of a quality-control procedure, eight circuit boards are checked, and the number of defectives is recorded.
​

A) {number 0 is recorded}, {number 1 is recorded}, {number 2 is recorded}, {number 3 is recorded}, {number 4 is recorded}, {number 5 is recorded}, {number 6 is recorded}, {number 7 is recorded}, {number 8 is recorded}, {number 9 is recorded}, {number 10 is recorded}
B) Ø
C) {number 8 is recorded}
D) {number 0 is recorded}, {number 1 is recorded}, {number 2 is recorded}, {number 3 is recorded}, {number 4 is recorded}, {number 5 is recorded}, {number 6 is recorded}, {number 7 is recorded}, {number 8 is recorded}

Question 52

The following breakdown of a total of 18,597 transportation fatalities that occured in 2007 was obtained from records compiled by the U.S. Department of Transportation (DOT). What is the probability that a victim randomly selected from this list of transportation fatalities for 2007 died in a train or a plane accident? Round answer to two decimal places.

A) 0.05
B) 0.11
C) 0.07
D) 0.08

Question 53

According to a survey of 176 retailers, 41% of them use electronic tags as protection against shoplifting and employee theft. If one of these retailers is selected at random, what is the probability that he or she uses electronic tags as anti-theft devices?

A) The probability is 0.40
B) The probability is 0.42
C) The probability is 0.41
D) The probability is 0.43

Question 54

Let , , and .
​
Are the events F and G complementary? Answer yes or no.

Question 55

In a survey of 700 likely voters, the following question was asked: Do you support using cameras to identify red-light runners? The results of the survey follow: What is the probability that a person in the survey selected at random favors using cameras to identify red-light runners?

A) 0.66
B) 0.71
C) 0.29
D) 0.61

Question 56

According to data obtained from the National Weather Service, 390 of the 442 people killed by lightning in the United States between 1985 and 1992 were men. (Job and recreational habits of men make them more vulnerable to lightning.) ​
Assuming that this trend holds in the future, what is the probability that a person killed by lightning is a male? Round your answer to the nearest thousandth.
​

A) The probability is 0.879
B) The probability is 0.882
C) The probability is 0.003
D) The probability is 0.885

Question 57

According to Mediamark Research, 86 million out of 179 million adults in the United States correct their vision by using prescription eyeglasses, bifocals, or contact lenses. (Some respondents use more than one type.) What is the probability that an adult selected at random from the adult population uses corrective lenses? Round your answer to the nearest thousandth.

A) The probability is 0.481
B) The probability is 0.479
C) The probability is 0.001
D) The probability is 0.480

Question 58

Let S be a sample space for an experiment and let N and L be events of this experiment. Show that the events N ∪ L and N^c ∩ L^c are mutually exclusive.
​
Hint: Use De Morgan's law.

Question 59

Let , , and .
​
Are the events F and G mutually exclusive? Answer yes or no.

Question 60

The percentage of the general population that has each blood type is shown in the table: Determine the probability distribution associated with these data.

A) Blood Type A B AB O
Population, % 0.36 0.11 0.05 0.48
B) Blood Type A B AB O
Population, % 0.4 0.11 0.03 0.46
C) Blood Type A B AB O
Population, % 0.46 0.03 0.11 0.4
D) Blood Type A B AB O
Population, % 0.42 0.13 0.03 0.42

Question 61

The grade distribution for a certain class is shown in the table. What is the probability that a student selected at random from this class received a passing grade (D or better)? Round to two decimal places, if necessary, and be sure to express answer in decimal form, not as a percentage.
The probability is __________.

Question 62

If a ball is selected at random from an urn containing three red balls, five white balls, and two blue balls, what is the probability that it will be a white ball? Round to two decimal places, if necessary, and be sure to express answer in decimal form, not as a percentage.
​
The probability is __________.

Question 63

A pair of fair dice is cast. What is the probability that the sum of the numbers shown uppermost is less than 6?

A) The probability is
B) The probability is
C) The probability is
D) The probability is

Question 64

According to data obtained from the National Weather Service, 387 of the 432 people killed by lightning in the United States between 1985 and 1992 were men. (Job and recreational habits of men make them more vulnerable to lightning.)
​
Assuming that this trend holds in the future, what is the probability that a person killed by lightning is a male? Round to three decimal places, if necessary, and be sure to express answer in decimal form, not as a percentage.
​
The probability is __________.

Question 65

According to Mediamark Research, 85 million out of 179 million adults in the United States correct their vision by using prescription eyeglasses, bifocals, or contact lenses. (Some respondents use more than one type.)
​
What is the probability that an adult selected at random from the adult population uses corrective lenses? Round to three decimal places, if necessary, and be sure to express answer in decimal form, not as a percentage.
​
The probability is __________ .

Question 66

According to a survey of 176 retailers, 51% of them use electronic tags as protection against shoplifting and employee theft.
​
If one of these retailers is selected at random, what is the probability that he or she uses electronic tags as anti-theft devices? Round to two decimal places, if necessary, and be sure to express answer in decimal form, not as a percentage.
​
The probability is __________.

Question 67

An opinion poll was conducted among a group of registered voters in a certain state concerning a proposition aimed at limiting state and local taxes. Results of the poll indicated that 31% of the voters favored the proposition, 37% were against it, and the remaining group were undecided. If the results of the poll are assumed to be representative of the opinions of the state's electorate, what is the probability that a registered voter selected at random from the electorate is undecided about the proposition?

A) 0.26
B) 0.28
C) 0.30
D) 0.32
E) 0.24

Question 68

Consider the composition of a three-child family in which the children were born at different times. Assume that a girl is as likely as a boy at each birth. What is the probability that there are two girls and a boy in the family?

A)
B)
C)
D)
E)

Question 69

What is the probability of arriving at a traffic light when it is red if the red signal is flashed for 35 sec, the yellow signal for 5 sec, and the green signal for 60 sec?

A) The probability is 0.30
B) The probability is 0.35
C) The probability is 0.45
D) The probability is 0.40

Question 70

The grade distribution for a certain class is shown in the table. What is the probability that a student selected at random from this class received a passing grade (D or better)?

A) The probability is 0.95
B) The probability is 0.99
C) The probability is 0.97
D) The probability is 0.93

Question 71

A study conducted by the Corrections Department of a certain state revealed that 162,883 people out of a total adult population of 1,713,709 were under correctional supervision (on probation, parole, or in jail). What is the probability that a person selected at random from the adult population in that state is under correctional supervision?

A)
B)
C)
D)
E)

Question 72

A study conducted by the Corrections Department of a certain state revealed that 166,756 people out of a total adult population of 1,714,697 were under correctional supervision (on probation, parole, or in jail).
​
What is the probability that a person selected at random from the adult population in that state is under correctional supervision? Round to three decimal places, if necessary, and be sure to express answer in decimal form, not as a percentage.
​
The probability is __________.

Question 73

The number of cars entering a tunnel leading to an airport in a major city over a period of 200 peak hours was observed and the following data were obtained.

What is the probability that more than 600 cars will enter the airport tunnel during a peak hour?

A)
B)
C)
D)
E)

Question 74

In a sweepstakes sponsored by Gemini Paper Products, 100,000 entries have been received. If 2 grand prize, 5 first prizes, 35 second prizes, and 600 third prizes are to be awarded, what is the probability that a person who has submitted one entry will win a prize? Round to five decimal places, if necessary, and be sure to express answer in decimal form, not as a percentage.
​
The probability is __________.

Question 75

In a sweepstakes sponsored by Gemini Paper Products, 100,000 entries have been received. If 3 grand prize, 5 first prizes, 30 second prizes, and 400 third prizes are to be awarded, what is the probability that a person who has submitted one entry will win a prize?

A) The probability is 0.00508
B) The probability is 0.01138
C) The probability is 0.00438
D) The probability is 0.00445

Question 76

What is the probability of arriving at a traffic light when it is red if the red signal is flashed for 15 sec, the yellow signal for 5 sec, and the green signal for 55 sec? Round to two decimal places, if necessary, and be sure to express answer in decimal form, not as a percentage.
​
The probability is __________.

Question 77

One light bulb is selected at random from a lot of 100 light bulbs, of which 6% are defective.
​
What is the probability that the light bulb selected is defective? Round to two decimal places, if necessary, and be sure to express answer in decimal form, not as a percentage.
​
The probability is __________.

Question 78

In a survey conducted in 2007 of 970 adults 18 years old and older, the following question was asked: How are American companies doing on protecting the environment compared with companies in other countries? The results are summarized below: If an adult in the survey selected at random, what is the probability that he or she said that American companies are equal or ahead on protecting the environment compared with companies in other countries? Round your answer to two decimal places.

A) 0.52
B) 0.45
C) 0.60
D) 0.65
E) 0.38

Question 79

Let be the sample space associated with an experiment having the following probability distribution: Find the probability of the event .

A) The probability is 0
B) The probability is
C) The probability is
D) The probability is

Question 80

Determine whether the given experiment has a sample space with equally likely outcomes. Two fair dice are cast, and the sum of the numbers appearing uppermost is recorded.

A) yes
B) no