Deck 4: Probability

Question 1

Express the indicated degree of likelihood as a probability value. "Your mother could not have died two years before you were born."

A) 1
B) 0.5
C) 0
D) 0.25

Answer 1

C

Question 2

Flip a coin twice. Create the sample space of possible outcomes.

A) {HT, TH}
B) {HH, HT, TH, TT}
C) {HH, HT, TT}
D) {HH, TT, HT, HT}

Answer 2

B

Question 3

The table below shows the soft drinks preferences of people in three age groups. If one of the 255 subjects is randomly selected, find the probability (in fractional form) that the person is over 40 and drinks cola.

Answer 3

B

Question 4

If a person is randomly selected, find the probability that his or her birthday is not in May. Ignore leap years.

Question 5

Select the correct interpretation of the probability of guessing the date of his birth, given that he told you in what month he was born. Interpret an event as significant if its probability is less than or equal to 0.05.

A) Significant
B) Not significant

Question 6

Select the correct interpretation of the probability of getting an 11 when a pair of dice is rolled. Interpret an event as significant if its probability is less than or equal to 0.05.

A) Significant at 0.055
B) Significant at 0.028
C) Not significant at 0.055
D) Not significant at 0.945

Question 7

Refer to the table which summarizes the results of testing for a certain disease. A test subject is randomly selected and tested for the disease. What is the probability the subject has the disease given that the test result is negative.

A) 0.972
B) 0.094
C) 0.028
D) 0.221

Question 8

Based on a recent poll, there is a 50-50 chance that a randomly selected adult has pierced ears. Express the indicated degree of likelihood as a probability value between 0 and 1.

Question 9

The following table contains data from a study of two airlines which fly to Small Town, USA. If one flight is selected, find P(on time and Upstate Airlines).

Question 10

Swinging Sammy Skor's batting prowess was simulated to get an estimate of the probability that Sammy will get a hit. Let 1 = HIT and 0 = OUT. The output from the simulation was as follows. Estimate the probability that he gets a hit.

A) 0.301
B) 0.286
C) 0.452
D) 0.476

Question 11

Some employers use lie detector tests to screen job applicants. Lie detector tests are not completely reliable. Suppose that in a lie detector test, 65% of lies are identified as lies and that 14% of true statements are also
Identified as lies. A company gives its job applicants a polygraph test, asking "Did you tell the truth on your job
Application?" Suppose that 93% of the job applicants tell the truth during the polygraph test. What is the
Probability that a person who fails the test was actually telling the truth?

A) 0.741
B) 0.259
C) 0.349
D) 0.14

Question 12

Assume that a study of 500 randomly selected airplane routes showed that 482 arrived on time. Select the correct interpretation of the probability of an airplane arriving late. Interpret an event as significant if its
Probability is less than or equal to 0.05.

A) Not significant at 0.036
B) Not significant at 0.964
C) Significant at 0.0036
D) Significant at 0.036

Question 13

Refer to the table which summarizes the results of testing for a certain disease. If one of the results is randomly selected, what is the probability that it is a false negative (test indicates the person does not have the disease when in fact they do)? What does this probability suggest about the accuracy of the test?

A) 0.0369; The probability of this error is low so the test is fairly accurate.
B) 0.0348; The probability of this error is low so the test is fairly accurate.
C) 0.0134; The probability of this error is low so the test is fairly accurate.
D) 0.591; The probability of this error is high so the test is not very accurate.

Question 14

In one town, 66% of adults have health insurance. What is the probability that 4 adults selected at random from the town all have health insurance? Round to the nearest thousandth if necessary.

A) 0.19
B) 0.66
C) 2.64
D) 0.061

Question 15

Determine whether the events are disjoint. Read a book by Mark Twain. Read about Tom Sawyer.

A) Yes
B) No

Question 16

Of 1232 people who came into a blood bank to give blood, 397 people had high blood pressure. Estimate the probability that the next person who comes in to give blood will have high blood pressure.

A) 0.373
B) 0.29
C) 0.322
D) 0.241

Question 17

A study conducted at a certain college shows that 65% of the school's graduates find a job in their chosen field within a year after graduation. Find the probability that 11 randomly selected graduates all find jobs in their
Chosen field within a year of graduating. Round to the nearest thousandth if necessary.

A) 0.013
B) 0.169
C) 0.009
D) 7.150

Question 18

Evaluate the expression

A) 4
B) 70
C) 1680
D) 2

Question 19

In a certain class of students, there are 11 boys from Wilmette, 7 girls from Wilmette, 5 boys from Winnetka, 4 girls from Winnetka, 4 boys from Glencoe, and 4 girls from Glencoe. If the teacher calls upon a student to
Answer a question, what is the probability that the student will be a boy?

A) 0.429
B) 0.314
C) 0.571
D) 0.71

Question 20

A firm uses trend projection and seasonal factors to simulate sales for a given time period. It assigns "0" if sales fall, "1" if sales are steady, "2" if sales rise moderately, and "3" if sales rise a lot. The simulator generates the following output. Estimate the probability that sales will rise at least moderately.

A) 0.613
B) 0.512
C) 0.516
D) 0.452

Question 21

When 100 engines are shipped, all of them are free of defects. Select a written description of the complement of the given event.

A) At most one of the engines is defective.
B) At least one of the engines is defective.
C) All of the engines are defective.
D) None of the engines are defective.

Question 22

Of the thirteen different women Calvin asks for a date, at least one of them accepts. Provide a written description of the complement of the given event.

A) None of the women accept Calvin's offer.
B) At most one of the women accepts Calvin's offer.
C) All but one woman accepts Calvin's offer.
D) All of the women accept Calvin's offer.

Question 23

The table below describes the smoking habits of a group of asthma sufferers. If one of the 1156 people is randomly selected, find the probability that the person is a man or a heavy smoker.

A) 0.554
B) 0.557
C) 0.596
D) 0.511

Question 24

In a recent year, 304 of the approximately 300,000,000 people in the United States were struck by lightning. Estimate the probability that a randomly selected person in the United States will be struck by lightning this
Year.

A) 0.0000101
B) 0.000000101
C) 0.00000101
D) 0.000101

Question 25

A multiple choice question has 18 possible answers, only one of which is correct. Is it "significant" to answer a question correctly if a random guess is made? Consider an event to be "significant" if its probability is less than
Or equal to 0.05.

A) Yes
B) No

Question 26

Evaluate the expression.

A) 120
B) 720
C) 7
D) 27

Question 27

Question 28

Refer to the table which summarizes the results of testing for a certain disease. A test subject is randomly selected and tested for the disease. What is the probability the subject has the disease given that the test result is negative?

A) 0.094
B) 0.972
C) 0.028
D) 0.221

Question 29

Results from a marijuana drug test study showed 143 subjects with positive test results including 24 false positive results. There were 157 negative results, including 3 false negative results. What is the probability that a
Randomly selected subject did not use marijuana?

A) 0.523
B) 0.533
C) 0.593
D) 0.477

Question 30

The manager of a bank recorded the amount of time each customer spent waiting in line during peak business hours one Monday. The frequency table below summarizes the results. If we randomly select one of the customers represented in the table, what is the probability that the waiting time is at
Least 12 minutes or between 8 and 15 minutes?

A) 0.727
B) 0.093
C) 0.651
D) 0.558

Question 31

Some employers use lie detector tests to screen job applicants. Lie detector tests are not completely reliable. Suppose that in a lie detector test, 65% of lies are identified as lies and that 14% of true statements are also
Identified as lies. A company gives its job applicants a polygraph test, asking "Did you tell the truth on your job
Application?". Suppose that 93% of the job applicants tell the truth during the polygraph test. What is the
Probability that a person who fails the test was actually telling the truth?

A) 0.741
B) 0.14
C) 0.259
D) 0.349

Question 32

In a certain town, 10% of people commute to work by bicycle. If a person is selected randomly from the town, what are the odds against selecting someone who commutes by bicycle?

A) 9 : 10
B) 1 : 9
C) 1 : 10
D) 9 : 1

Question 33

Fred and Ed each have a bag of candy containing a lemon drop (LD), a cherry drop(CD), and a lollipop (LP). Each takes out a piece from their own bag and eats it. What are the possible pairs of candies eaten?

A) LD-LD, CD-LD, LP-LP, LD-CD, CD-CD, LD-LP, LP-CD, CD-LP, LP-LD
B) LD-LD, CD-LD, LP-LP, LD-LP, CD-CD, LD-LP, LP-CD, CD-LD, LP-LD
C) CD-LD, LD-LP, LP-CD, LP-LP, LD-LD
D) LD-CD, LD-CD, LD-CD, LD-LP, LD-LP, LD-LP, CD-LP, CD-LP, CD-LP

Question 34

Determine whether the events are disjoint. Finding a ten dollar bill on the sidewalk.
Finding a ten dollar bill on the grass.

A) Yes
B) No

Question 35

Suppose you are playing a game of chance. If you bet $5 on a certain event, you will collect $115 (including your $5 bet) if you win. Find the odds used for determining the payoff.

A) 22 : 1
B) 1 : 22
C) 23 : 1
D) 115 : 120

Question 36

If you drew one card from a standard deck, would it be "significant" to draw a 5? Answer the question, considering an event to be "significant" if its probability is less than or equal to 0.05.

A) Yes
B) No

Question 37

Determine whether the events are disjoint. Get a full-time day job as a teller with a bank.
Get a full time day job as a cashier at a store.

A) Yes
B) No

Question 38

Find the indicated probability. Find the probability that 3 randomly selected people all have the same birthday. Ignore leap years. Round to eight decimal places.

A) 0.0082
B) 0.3333
C) 0.00000002
D) 0.00000751

Question 39

Which of the following statements is not true?

A) If P(A) = 0, then the probability of the complement of A is 1.
B) If the probability of an event occurring is 0, then it is impossible for that event to occur.
C) If the probability of an event occurring is 1.5, then it is certain that event will occur.
D) Probability can never be a negative value.

Question 40

The table below shows the soft drinks preferences of people in three age groups. If one of the 255 subjects is randomly selected, find the probability that the person drinks root beer given that they are over 40.

Question 41

Discuss the advantages and disadvantages of odds.

Question 42

In the Texas Pick 3 Lottery, you can bet $1 by selecting the exact order of three digits between 0 and 9 inclusive,
so the probability of winning is f the same three numbers are draw in the same order, you collect $500,
so your net profit is $499. Find the actual odds against winning and the payoff odds. The website indicates that
the odds are 1:1000 for this bet. Is this an accurate description?

Question 43

In a recent year, 304 of the approximately 300,000,000 people in the United States were struck by lightning. The
probability that a randomly selected person in the United States will be struck by lightning this year is
0.00000101. Is a golfer reasoning correctly if he or she is caught out in a thunderstorm and does not seek shelter
from lightening because the probability of being struck is so small?

Question 44

Use technology to develop a simulation of the given problem (100 trials). Describe the simulation, then estimate the
probability based on its results.
The probability of getting at least two boys in a family of seven children.

Question 45

Interpret a probability of 0.002 of an event occurring in terms of odds (one in some value, such as 1/10) and
being a significant or not a significant event.

Question 46

In one method of a procedure called acceptance sampling, a sample of items is randomly selected without
replacement and the entire batch is accepted if every item in the sample is ok. Among 810 airport baggage
scales, 102 are defective (based on data from the NY Department of Consumer Affairs). If four of the scales are
randomly selected and tested, what is the probability that the entire bath will be accepted? Is this scheme likely
to detect the large number of defects?

Question 47

Use technology to develop a simulation of the given problem (100 trials). Describe the simulation, then estimate the
probability based on its results.
The probability of getting a total of 15 when four dice are thrown.

Question 48

A statistics student plans to use a TI-84 Plus calculator on her final exam. From past experience, she estimates
there is a 0.92 probability that the calculator will work on any given day. Because the final exam is so important,
she plans to bring in two calculators in case one loses power. Does she gain much by bringing in the backup
calculator? Use the probability that she will be able to complete her exam with a working calculator.

Question 49

Tomorrow Freddy is playing in an important soccer game. He reasons that there are three possible outcomes
(they could win, tie, or lose) so the probability of winning must be 1 /3. Is this reasoning correct? Why or why
not?

Question 50

Given that the following statement is incorrect, rewrite it correctly: "The probability of being born a boy is

Question 51

If a game were "fair," the payoff on a bet would be the same as the odds for the event. In one game, the odds for
winning are 1:13. If the game were "fair," what would the payoff be for a $5 bet? Of course, games in casinos are
designed to make a profit for the casino investors. Supposing the casino makes the payoff at 1:11 odds, what
profit does the casino make on your winning bet?

Question 52

Compare probabilities and odds. How can you convert odds to probabilities?

Question 53

The probability of a randomly selected car crashing during a year is 0.0423 (based on data from the Statistical
Abstract of the United States). If a family has three cars, find the probability that at least one of them has a crash
during the year. Is there any reason why this probability might be wrong?

Question 54

Assume that a crucial machine part has a 5% rate of failure in six months, based on company data. Compare the
probability of having a single part fail during a six month period to the probability of having a second
independent backup part and having both of them fail in 6 months. Describe the improved reliability gained
with a backup part.

Question 55

Discuss the range of possible values for probabilities. Give examples to support this.

Question 56

Use technology to develop a simulation of the given problem (100 trials). Describe the simulation, then estimate the
probability based on its results.
The probability that when 75 people are surveyed, at least five of them have the same birth date. (Ignore leap years.)

Question 57

Describe the process for making a tree diagram and give an example.

Question 58

On an exam on probability concepts, Sue had an answer of for one problem. Explain how she knew that this
result was incorrect.

Question 59

What important question must you answer before computing an "or" probability? How does the answer
influence your computation?

Question 60

An author has six different books in print. If those six books are stacked in a random order, what is the
probability that they are arranged in alphabetical order from top to bottom? How about seven different books?

Question 61

What is the probability of an event that is certain to occur?

A) 0.95
B) 1
C) 0.99
D) 0.5

Question 62

Find the indicated probability.
A class consists of 27 women and 32 men. If a student is randomly selected, what is the probability that the student is a woman?

Question 63

On a multiple choice test with four possible answers for each question, what is the probability of answering a question correctly if you make a random guess?

Question 64

Find the indicated probability.
A sample space consists of 38 separate events that are equally likely. What is the probability of each?

Question 65

"You have one chance in ten of winning the race."

A) 0.5
B) 1
C) 0.10
D) 0.90

Question 66

"There is a 40% chance of rain tomorrow."

A) 0.40
B) 40
C) 0.60
D) 4

Question 67

Find the indicated probability.
Two 6-sided dice are rolled. What is the probability that the sum of the two numbers on the dice will be 3?

Question 68

What is the probability of an impossible event?

A) -1
B) 1
C) 0.1
D) 0

Question 69

"It will definitely turn dark tonight."

A) 1
B) 0.5
C) 0.67
D) 0.30

Question 70

Find the indicated probability.
On a multiple choice test, each question has 6 possible answers. If you make a random guess on the first question, what is the probability that you are correct?

Question 71

"Your mother could not have died two years before you were born."

A) 0
B) 1
C) 0.5
D) 0.25

Question 72

Find the indicated probability.
A bag contains 6 red marbles, 3 blue marbles, and 5 green marbles. If a marble is randomly selected from the bag, what is the probability that it is blue?

Question 73

Find the indicated probability.
A die with 12 sides is rolled. What is the probability of rolling a number less than 11?

Question 74

Find the indicated probability.
In a poll, respondents were asked whether they had ever been in a car accident. 215 respondents indicated that they had been in a car accident and 449 respondents said that they had not been in a car accident. If one of these
Respondents is randomly selected, what is the probability of getting someone who has been in a car accident?
Round to the nearest thousandth, if necessary.

A) 0.479
B) 0.324
C) 0.676
D) 0.005

Question 75

Find the indicated probability.
If a person is randomly selected, find the probability that his or her birthday is in May. Ignore leap years.

Question 76

Which of the following cannot be a probability?

Question 77

Find the indicated probability.
In a certain class of students, there are 11 boys from Wilmette, 3 girls from Kenilworth, 9 girls from Wilmette, 5 boys from Glencoe, 5 boys from Kenilworth and 7 girls from Glencoe. If the teacher calls upon a student to
Answer a question, what is the probability that the student will be from Kenilworth?

A) 0.075
B) 0.267
C) 0.238
D) 0.2

Question 78

Which of the following cannot be a probability?

A) 0
B) -1
C) 1
D)

Question 79

"You cannot determine the exact decimal-number value of

A) 0
B) 0.5
C) 1
D) 3.14

Question 80

Find the indicated probability.
The data set represents the income levels of the members of a country club. Find the probability that a randomly selected member earns at least $77,000. Round your answers to the nearest tenth.

A) 0.6
B) 0.4
C) 0.8
D) 0.7