Deck 4: Probability

Question 1

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) 0.061
C) 0.66
D) 2.64

Answer 1

A

Question 2

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) 0.259
B) 0.349
C) 0.14
D) 0.741

Answer 2

D

Question 3

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

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

Answer 3

B

Question 4

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 5

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) 0.028
B) 0.094
C) 0.221
D) 0.972

Question 6

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) 0.241
C) 0.322
D) 0.29

Question 7

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

A) Yes
B) No

Question 8

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

Question 9

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 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) 0.286
B) 0.301
C) 0.476
D) 0.452

Question 11

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) 0.009
C) 0.169
D) 7.150

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

Question 13

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

Question 14

The table below shows the soft drinks preferences of people in three age groups.

Question 15

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) 0.71
B) 0.429
C) 0.571
D) 0.314

Question 16

Evaluate the expression .

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

Question 17

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) 0.516
C) 0.512
D) 0.452

Question 18

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 19

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

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

Question 20

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

Question 21

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) 0.00000751
D) 0.00000002

Question 22

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) 0.558
B) 0.651
C) 0.093
D) 0.727

Question 23

Evaluate the expression.

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

Question 24

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

Question 25

Question 26

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

Question 27

A 6-sided die is rolled. Find P(3 or 5).

Question 28

Which of the following statements is not true?

A) If the probability of an event occurring is 0, then it is impossible for that event to occur…
B) If P(A) = 0, then the probability of the complement of A is 1.
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 29

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

Question 30

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 31

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 32

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 33

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) 0.477
C) 0.593
D) 0.533

Question 34

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

Question 35

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) 0.511
B) 0.554
C) 0.596
D) 0.557

Question 36

A multiple choice question has 18 possible answers, only one of which is correct. "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 37

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) 0.349
B) 0.14
C) 0.741
D) 0.259

Question 38

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) 0.028
C) 0.972
D) 0.221

Question 39

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) 0.00000101
C) 0.000000101
D) 0.000101

Question 40

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

Question 41

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 42

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 43

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 1/1000. If 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 44

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 45

Given that the following statement is incorrect, rewrite it correctly: "The probability of
being born a boy is 50-50."

Question 46

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

Question 47

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

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

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 50

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 51

Discuss the advantages and disadvantages of odds.

Question 52

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

Question 53

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

Question 54

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

Question 55

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 56

Use technology to develop a simulation of the given problem (100 trials).
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

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

Question 58

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 59

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 60

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