Question 1

Estimate the probability of the event.
-A polling firm, hired to estimate the likelihood of the passage of an up-coming referendum, obtained the set of survey responses to make its estimate. The encoding system for the data is: $0 =$ FOR, 1 = AGAINST . If the referendum were held today, estimate the probability that it would pass.
$$0,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0,0,0,1,0$$
A) 0.4
B) 0.5
C) 0.65
D) 0.6

Accepted Answer

The answer of Estimate the probability of the event.
-A polling...

Question 2

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

A) $\frac { 334 } { 365 }$

B) $\frac { 31 } { 334 }$

C) $\frac { 11 } { 12 }$

D) $\frac { 31 } { 365 }$

Accepted Answer

There are 31 days in May, so the probability of a birthday being in May is $\frac{31}{365}$. Therefore, the probability of a birthday not being in May is $1 - \frac{31}{365} = \frac{334}{365}$.

Question 3

Find the indicated probability. Express your answer as a simplified fraction unless otherwise noted.
-The following table contains data from a study of two airlines which fly to Small Town, USA. $\begin{array}{l|cc} 
&\text { Number of flights } & \text {Number of flights } \
& \text { which were on time } & \text { which were late } \
\hline \text { Podunk Airlines } & 33 & 6 \
\text { Upstate Airlines } & 43 & 5
\end{array}$
If one of the 87 flights is randomly selected, find the probability that the flight selected arrived on time.

A) $\frac { 43 } { 87 }$

B) $\frac { 76 } { 87 }$

C) $\frac { 11 } { 76 }$

D) None of the above is correct.

Accepted Answer

The probability of selecting a flight that arrived on time is the number of flights that arrived on time divided by the total number of flights. From the table, we see that 33 + 43 = 76 flights arrived on time out of a total of 87 flights. Therefore, the probability of selecting a flight that arrived on time is 76/87.

Question 4

From the information provided, create the sample space of possible outcomes.
-Flip a coin three times. 
A) HTT THT ?TH ??? ??? ?TT
B) HHH HHT HTH HTT THH THT TTH TTT
C) HHH HTT HTH TTT HTT THH HHT THT
D) ??? ??? ??? ??? ??? ??? ???

Accepted Answer

The sample space for flipping a coin three times is all possible combinations of heads (H) and tails (T). There are 2 possible outcomes for each flip, so there are 2^3 = 8 possible outcomes overall. These outcomes are: HHH, HHT, HTH, HTT, THH, THT, TTH, TTT.

Question 5

Answer the question, considering an event to be "unusual" if its probability is less than or equal to 0.05.
-Assume that one student in your class of 31 students is randomly selected to win a prize. Would it be "unusual" for you to win?
A) Yes
B) No

Accepted Answer

The answer of Answer the question, considering an event to...

Question 6

Find the indicated probability.
-The table below describes the smoking habits of a group of asthma sufferers. $\begin{array}{r|ccccc} 
& \text { Occasional } & \begin{array}{c}
\text { Regular } \
\text { smoker }
\end{array} & \begin{array}{c}
\text { Heavy } \
\text { smoker }
\end{array} & \text { smoker } & \text { Total } \
\hline \text { Men } & 380 & 48 & 63 & 42 & 533 \
\text { Women } & 360 & 34 & 90 & 47 & 531 \
\text { Total } & 740 & 82 & 153 & 89 & 1064
\end{array}$ If one of the 1064 people is randomly selected, find the probability that the person is a man or a heavy smoker.
A) 0.545
B) 0.506
C) 0.585
D) 0.472

Accepted Answer

The probability that the person is a man is 533/1064 = 0.501. The probability that the person is a heavy smoker is 153/1064 = 0.144. The probability that the person is a man or a heavy smoker is 0.501 + 0.144 - 0.003 = 0.545.

Question 7

A sample space consists of 154 separate events that are equally likely. What is the probability of each?

A) $\frac { 1 } { 154 }$

B) 1

C) 154

D) 0

Accepted Answer

The probability of each event in a sample space with equally likely events is the reciprocal of the total number of events, which is $\frac{1}{154}$.

Question 8

Refer to the table which summarizes the results of testing for a certain disease. $\begin{array}{l|cc} 
& \text { Positive Test Result } & \text { Negative Test Result } \
\hline \text { Subject has the disease } & 85 & 7 \
\text { Subject does not have the disease } & 27 & 85
\end{array}$ 
A test subject is randomly selected and tested for the disease. What is the probability the subject does not have the disease given that the test result is positive?
A) 0.241
B) 0.108
C) 0.731
D) 0.759

Accepted Answer

The answer of Refer to the table which summarizes the...

Question 9

Use Bayes' theorem to find the indicated probability.
-In one town, 7% of 18-29 year olds own a home, as do 27% of 30-50 year olds and 52% of those over 50. According to a recent census taken in the town, 27.5% of adults in the town are 18-29 years old, 38.4% are 30-50 years old, and 34.1% are over 50. If an adult is selected at random from the town and found to be a home-owner, what is the probability that they are aged between 30 and 50?
A) 0.384
B) 0.345
C) 0.27
D) 0.104

Accepted Answer

Using Bayes' theorem, the probability that a homeowner is aged 30-50 is calculated by finding the probability of being 30-50 and a homeowner divided by the total probability of being a homeowner.

Question 10

A pollster wants to minimize the effect the order of the questions has on a person's response to a survey. How many different surveys are required to cover all possible arrangements if there are 6 questions on the survey?
A) 36
B) 120
C) 720
D) 6

Accepted Answer

The number of different arrangements of 6 questions is given by 6! (6 factorial), which is 720.

Question 11

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. $\begin{array}{llcc}
0&1&0&2&0&0&0&1&0&3&2&0&0&0&0&2&1&2&3&1&2&0&2&0&3&0&0&2&1&0&1
\end{array}$
 Estimate the probability that sales will rise moderately.
A) 0.312
B) 0.226
C) 0.258
D) 0.233

Accepted Answer

The answer of A firm uses trend projection and seasonal...

Question 12

The organizer of a television show must select 5 people to participate in the show. The participants will be selected from a list of 21 people who have written in to the show. If the participants are selected randomly, what is the probability that the 5 youngest people will be selected?

A) $\frac { 1 } { 2,441,880 }$

B) $\frac { 1 } { 20,349 }$

C) $\frac { 8 } { 21 }$

D) $\frac { 1 } { 120 }$

Accepted Answer

The answer of The organizer of a television show must...

Question 13

Determine whether the events are disjoint.
-Go to a formal dinner affair. Wear blue jeans.
A) Yes
B) No

Accepted Answer

The events of going to a formal dinner affair and wearing blue jeans are disjoint because a formal dinner affair typically requires formal attire, while blue jeans are considered casual attire. Therefore, one cannot attend a formal dinner affair wearing blue jeans, making these events mutually exclusive.

Question 14

100 employees of a company are asked how they get to work and whether they work full time or part time. The figure below shows the results. If one of the 100 employees is randomly selected, find the probability of getting someone who carpools, someone who cycles to work, or someone who works part time. 
 
1. Public transportation: 10 full time, 8 part time
2) Bicycle: 4 full time, 4 part time
3) Drive alone: 25 full time, 30 part time
4) Carpool: 10 full time, 9 part time

A) 0.52
B) 0.65
C) 0.27
D) 0.78

Accepted Answer

The answer of 100 employees of a company are asked...

Question 15

Find the indicated probability. Round to the nearest thousandth.
-In a blood testing procedure, blood samples from 5 people are combined into one mixture. The mixture will only test negative if all the individual samples are negative. If the probability that an individual sample tests positive is 0.09, what is the probability that the mixture will test positive?
A) 0.376
B) 1.00
C) 0.00000590
D) 0.624

Accepted Answer

The answer of Find the indicated probability. Round to the...

Question 16

The library is to be given 5 books as a gift. The books will be selected from a list of 20 titles. If each book selected must have a different title, how many possible selections are there?
A) 3,200,000
B) 100
C) 15,504
D) 1,860,480

Accepted Answer

The number of ways to select 5 books from 20 different titles is given by the combination formula C(n, k) = n! / (k!(n-k)!), where n is the total number of titles and k is the number of books to select. Here, C(20, 5) = 20! / (5! * 15!) = 15,504.

Question 17

Provide a written description of the complement of the given event.
-When 100 engines are shipped, all of them are free of defects.
A) At most one of the engines is defective.
B) At least one of the engines is defective.
C) None of the engines are defective.
D) All of the engines are defective.

Accepted Answer

The complement of the event "all of them are free of defects" is "at least one of the engines is defective."

Question 18

Find the indicated probability.
-A IRS auditor randomly selects 3 tax returns from 54 returns of which 15 contain errors. What is the probability that she selects none of those containing errors? Round to four decimal places.
A) 0.3767
B) 0.0214
C) 0.0183
D) 0.3684

Accepted Answer

The answer of Find the indicated probability.
-A IRS auditor randomly...

Question 19

If you are told that a randomly selected mystery person was born in the 1990's, what is the probability of guessing his/her exact birth date (including year)?

A) $2.738 \times 10 ^ { - 3 }$
B) $2.737 \times 10 ^ { - 3 }$
C) $2.740 \times 10 ^ { - 4 }$
D) $2.738 \times 10 ^ { - 4 }$

Accepted Answer

There are 10 years in the 1990s, and each year has 365 days, except for 1992, 1996, and 2000, which are leap years with 366 days. This totals to 3652 days. The probability of guessing the exact birth date is $ \frac{1}{3652} \approx 2.738 \times 10^{-4} $.

Question 20

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

A) $\frac { 1 } { 2 }$

B) $\frac { 1 } { 18 }$

C) $\frac { 17 } { 18 }$

D) 2

Accepted Answer

There are 36 possible outcomes when rolling two 6-sided dice. The sum of 3 can occur in two ways: (1,2) and (2,1). Thus, the probability is $\frac{2}{36} = \frac{1}{18}$.

Quiz 4: Probability

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

From the information provided, create the sample space of possible outcomes. -Flip a coin three times.

Answer the question, considering an event to be "unusual" if its probability is less than or equal to 0.05. -Assume that one student in your class of 31 students is randomly selected to win a prize. Would it be "unusual" for you to win?

A sample space consists of 154 separate events that are equally likely. What is the probability of each?

A pollster wants to minimize the effect the order of the questions has on a person's response to a survey. How many different surveys are required to cover all possible arrangements if there are 6 questions on the survey?

The organizer of a television show must select 5 people to participate in the show. The participants will be selected from a list of 21 people who have written in to the show. If the participants are selected randomly, what is the probability that the 5 youngest people will be selected?

Determine whether the events are disjoint. -Go to a formal dinner affair. Wear blue jeans.

The library is to be given 5 books as a gift. The books will be selected from a list of 20 titles. If each book selected must have a different title, how many possible selections are there?

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

Find the indicated probability. -A IRS auditor randomly selects 3 tax returns from 54 returns of which 15 contain errors. What is the probability that she selects none of those containing errors? Round to four decimal places.

If you are told that a randomly selected mystery person was born in the 1990's, what is the probability of guessing his/her exact birth date (including year) ?

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