Deck 4: Basic Probability

Question 1

The probability that house sales will increase in the next 6 months is estimated to be 0.25. The probability that the interest rates on housing loans will go up in the same period is estimated to be 1.. The probability that house sales or interest rates will go up during the next 6 months is estimated to be 0.89. The events of increase in house sales and increase in interest rates in the next 6 months are
A) collectively exhaustive.

A) mutually exclusive.
B) statistically independent.
D) none of the above

Answer 1

D

Question 2

If either event A or event B must occur, then events A and B are said to be

A) mutually exclusive.
B) collectively exhaustive.
C) statistically independent.
D) none of the above

Answer 2

B

Question 3

All the events in the sample space that are not part of the specified event are called

A) simple events.
B) the complement of the event.
C) joint events.
D) the sample space.

Answer 3

B

Question 4

A company has 2 machines that produce widgets. An older machine produces 23% defective widgets, while the new machine produces only 8% defective widgets. In addition, the new machine produces 3 times as many widgets as the older machine does. Given a randomly chosen widget was tested and found to be defective, what is the probability it was produced by the new machine?

A) 0.511
B) 0.489
C) 0.15
D) 0.08

Question 5

If two events are mutually exclusive and collectively exhaustive, what is the probability that one or the other occurs?

A) 0
B) 1.00
C) 0.50
D) cannot be determined from the information given

Question 6

According to a survey of American households, the probability that the residents own 2 cars if annual household income is over $25,000 is 80%. Of the households surveyed, 60% had incomes over $25,000 and 70% had 2 cars. What is the probability that the residents of a household do not own 2 cars and have an income over $25,000 a year?

A) 0.18
B) 0.48
C) 0.22
D) 0.12

Question 7

The probability that a new advertising campaign will increase sales is assessed as being 0.80. The probability that the cost of developing the new ad campaign can be kept within the original budget allocation is 0.40. Assuming that the two events are independent, what is the probability that the cost is kept within budget or the campaign will increase sales?

A) 0.32
B) 0.88
C) 0.20
D) 0.68

Question 8

If two events are collectively exhaustive, what is the probability that one or the other occurs?

A)1.00
B) 0.50
C) 0
D) cannot be determined from the information given

Question 9

The closing price of a company's stock tomorrow can be lower, higher or the same as today's closing price. Based on the closing price of the stock collected over the last month, 25% of the days the closing price was higher than previous day's closing price, 45% was lower than previous day's and 30% was the same as previous day's. Based on this information, the probability that tomorrow's closing price will be higher than today's is 25%. This is an example of using which of the following probability approach?

A) empirical classical probability
B) subjective probability
C) a priori classical probability
D) conditional probability

Question 10

The probability that a new advertising campaign will increase sales is assessed as being 0.80. The probability that the cost of developing the new ad campaign can be kept within the original budget allocation is 0.40. Assuming that the two events are independent, what is the probability that neither the cost is kept within budget nor the campaign will increase sales?

A) 0.88
B) 0.12
C) 0.68
D) 0.32

Question 11

The probability that a new advertising campaign will increase sales is assessed as being 0.80. The probability that the cost of developing the new ad campaign can be kept within the original budget allocation is 0.40. Assuming that the two events are independent, what is the probability that the cost is kept within budget and the campaign will increase sales?

A) 0.40
B) 0.88
C) 0.32
D) 0.20

Question 12

$$\text { TABLE 4-2 }$$ An alcohol awareness task force at a Big-Ten university sampled 200 students after the midterm to ask them whether they went bar hopping the weekend before the midterm or spent the weekend studying, and whether they did well or poorly on the midterm. The following result was obtained.
$$\begin{array}{l}\begin{array} { lcc} &\text { Did Well on Midterm}& \text {Did Poorlyon Midterm }\\\hline \text { Studyingfor Exam } & 80 & 20 \\\text { Went Bar Hopping } & 30 & 70\end{array}\end{array}$$


-Referring to Table 4-2, the events "Did Well on Midterm" and "Studying for Exam" are

A) collective exhaustive.
B) statistically dependent.
C) mutually exclusive.
D) none of the above

Question 13

If the outcome of event A is not affected by event B, then events A and B are said to be

A) collectively exhaustive.
B) mutually exclusive.
C) statistically independent.
D) none of the above

Question 14

$$\text { TABLE 4-1 }$$ Mothers Against Drunk Driving is a very visible group whose main focus is to educate the public about the harm caused by drunk drivers. A study was recently done that emphasized the problem we all face with drinking and driving. Four hundred accidents that occurred on a Saturday night were analyzed. Two items noted were the number of vehicles involved and whether alcohol played a role in the accident. The numbers are shown below:
$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Number of Vehicles Involved }$
$\begin{array}{lccccc}\text { Did alcohol playa role? } & 1 && 2 & 3 & \text { Totals } \\\hline \text { Yes } & 50 & & 100 & 20 & 170 \\\hline \text { No } & 25 & & 175 & 30 & 230 \\ \text { Totals } & 75 && 275 & 50 & 400 &\\\hline \end{array}$


-Referring to Table 4-1, given alcohol was involved, what proportion of accidents involved a single vehicle?

A) 120/400 or 30%
B) 50/170 or 29.41%
C) 120/170 or 70.59%
D) 50/75 or 66.67%

Question 15

The collection of all possible events is called

A) the null set.
B) a simple probability.
C) a joint probability.
D) a sample space.

Question 16

A business venture can result in the following outcomes (with their corresponding chance of occurring in parentheses): Highly Successful (10%), Successful (25%), Break Even (25%), Disappointing (20%), and Highly Disappointing (?). If these are the only outcomes possible for the business venture, what is the chance that the business venture will be considered Highly Disappointing?

A) 20%
B) 15%
C) 25%
D) 10%

Question 17

The closing price of a company's stock tomorrow can be lower, higher or the same as today's closing price. After evaluating all the information available on the company's fundamentals and the economic environment, an analyst has determined that the probability that tomorrow's closing price will be higher than today's is determined to be 25%. This is an example of using which of the following probability approach?

A) a priori classical probability
B) subjective probability
C) conditional probability
D) empirical classical probability

Question 18

TABLE 4-1
Mothers Against Drunk Driving is a very visible group whose main focus is to educate the public about the harm caused by drunk drivers. A study was recently done that emphasized the problem we all face with drinking and driving. Four hundred accidents that occurred on a Saturday night were analyzed. Two items noted were the number of vehicles involved and whether alcohol played a role in the accident. The numbers are shown below:
$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Number of Vehicles Involved }$
$\begin{array}{lccccc}\text { Did alcohol playa role? } & 1 & &2 & 3 & \text { Totals } \\\hline \text { Yes } & 50 & & 100 & 20 & 170 \\\hline \text { No } & 25 & & 175 & 30 & 230 \\ \text { Totals } & 75 & &275 & 50 & 400 &\\\hline \end{array}$


-Referring to Table 4-1, what proportion of accidents involved alcohol or a single vehicle?

A) 25/400 or 6.25%
B) 195/400 or 48.75%
C) 50/400 or 12.5%
D) 245/400 or 61.25%

Question 19

If event A and event B cannot occur at the same time, then events A and B are said to be

A) mutually exclusive.
B) collectively exhaustive.
C) statistically independent.
D) none of the above

Question 20

The employees of a company were surveyed on questions regarding their educational background and marital status. Of the 600 employees, 400 had college degrees, 100 were single, and 60 were single college graduates. What is the probability that an employee of the company does not have a college degree?

A) 0.33
B) 0.67
C) 0.75
D) 0.10

Question 21

TABLE 4-2
An alcohol awareness task force at a Big-Ten university sampled 200 students after the midterm to ask them whether they went bar hopping the weekend before the midterm or spent the weekend studying, and whether they did well or poorly on the midterm. The following result was obtained.
$$\begin{array}{l}\begin{array} { lcc} &\text { Did Well on Midterm}& \text {Did Poorlyon Midterm }\\\hline \text { Studyingror Exam } & 80 & 20 \\\text { Went Bar Hopping } & 30 & 70\end{array}\end{array}$$


-Referring to Table 4-2, what is the probability that a randomly selected student did well on the midterm or went bar hopping the weekend before the midterm?

A) 30/200 or 15%
B) (30 + 70)/200 or 50%
C) (80 + 30 + 70)/200 or 90%
D) (80 + 30)/200 or 55%

Question 22

A recent survey of banks revealed the following distribution for the interest rate being charged on a home loan (based on a 30-year mortgage with a 10% down payment). If a bank is selected at random from this distribution, what is the chance that the interest rate charged on a home loan will exceed 8.0%?
$$\begin{array} { l | l l l l l } \text { Interest Rate } & 7.0 \% & 7.5 \% & 8.0 \% & 8.5 \%& > 8.5 \% \\\hline \text { Probability } & 0.12 & 0.23 & 0.24 & 0.35 & 0.06\end{array}$$

A) 0.06
B) 0.59
C) 0.41
D) 1.00

Question 23

If two equally likely events A and B are collectively exhaustive, what is the probability that event A occurs?

A) 0
B) 1.00
C) 0.50
D) cannot be determined from the information given

Question 24

The employees of a company were surveyed on questions regarding their educational background and marital status. Of the 600 employees, 400 had college degrees, 100 were single, and 60 were single college graduates. What is the probability that an employee of the company is married and has a college degree?

A) 500/600
B) 340/600
C) 400/600
D) 40/600

Question 25

If two events are independent, what is the probability that they both occur?
A) 0

A) 1.00
B) 0.50
B) cannot be determined from the information given

Question 26

The probability that house sales will increase in the next 6 months is estimated to be 0.25. The probability that the interest rates on housing loans will go up in the same period is estimated to be 1.. The probability that house sales or interest rates will go up during the next 6 months is estimated to be 0.89. The events of increase in house sales and no increase in house sales in the next 6 months are

A) statistically independent.
B) collectively exhaustive.
C) mutually exclusive.
D) both B and C

Question 27

If two events are mutually exclusive, what is the probability that both occur at the same time?

A) 1.00
B) 0
C) 0.50
D) cannot be determined from the information given

Question 28

TABLE 4-1
Mothers Against Drunk Driving is a very visible group whose main focus is to educate the public about the harm caused by drunk drivers. A study was recently done that emphasized the problem we all face with drinking and driving. Four hundred accidents that occurred on a Saturday night were analyzed. Two items noted were the number of vehicles involved and whether alcohol played a role in the accident. The numbers are shown below:
$$\begin{array}{l}\text { Number of Vehicles Involved }\\\begin{array} { l c c c c } \text { Did alcohol play a role? } & 1 & 2 & 3 & \text { Totals } \\\hline \text { Yes } & 50 & 100 & 20 & 170 \\\hline \text { No } & 25 & 175 & 30 & 230 \\\text { Totals } & 75 & 275 & 50 & 400 \\\hline\end{array}\end{array}$$

-Referring to Table 4-1, what proportion of accidents involved more than one vehicle?

A) 50/400 or 12.5%
B) 325/400 or 81.25%
C) 75/400 or 18.75%
D) 275/400 or 68.75%

Question 29

According to a survey of American households, the probability that the residents own 2 cars if annual household income is over $25,000 is 80%. Of the households surveyed, 60% had incomes over $25,000 and 70% had 2 cars. What is the probability that the residents do not own 2 cars if annual household income is not over $25,000?

A) 0.45
B) 0.70
C) 0.12
D) 0.18

Question 30

The probability that house sales will increase in the next 6 months is estimated to be 0.25. The probability that the interest rates on housing loans will go up in the same period is estimated to be 0.74. The probability that house sales or interest rates will go up during the next 6 months is estimated to be 0.89. What is the probability that house sales will increase but interest rates will not during the next 6 months?

A) 0.89
B) 0.15
C) 0.065
D) 0.51

Question 31

The probability that house sales will increase in the next 6 months is estimated to be 0.25. The probability that the interest rates on housing loans will go up in the same period is estimated to be 0.74. The probability that house sales or interest rates will go up during the next 6 months is estimated to be 0.89. What is the probability that neither house sales nor interest rates will increase during the next 6 months?

A) 0.90
B) 0.11
C) 0.195
D) 0.89

Question 32

TABLE 4-1
Mothers Against Drunk Driving is a very visible group whose main focus is to educate the public about the harm caused by drunk drivers. A study was recently done that emphasized the problem we all face with drinking and driving. Four hundred accidents that occurred on a Saturday night were analyzed. Two items noted were the number of vehicles involved and whether alcohol played a role in the accident. The numbers are shown below:
$$\begin{array}{l}\text { Number of Vehicles Involved }\\\begin{array} { l c l l l c } \hline \text { Did alcohol playa role? } & 1 & 2 & 3 & \text { Totals } \\\hline \text { Yes } & 50 & 100 & 20 & 170 \\\hline \text { No } & 25 & 175 & 30 & 230 \\\text { Totals } & 75 & 275 & 50 & 400 \\\hline\end{array}\end{array}$$

-Referring to Table 4-1, given that alcohol was not involved, what proportion of the accidents were single vehicle?

A) 25/75 or 33.33%
B) 50/170 or 29.41%
C) 50/75 or 66.67%
D) 25/230 or 10.87%

Question 33

According to a survey of American households, the probability that the residents own 2 cars if annual household income is over $25,000 is 80%. Of the households surveyed, 60% had incomes over $25,000 and 70% had 2 cars. What is the probability that annual household income is over $25,000 if the residents of a household own 2 cars?

A) 0.48
B) 0.50
C) 0.69
D) 0.42

Question 34

If two events are collectively exhaustive, what is the probability that both occur at the same time?

A) 1.00
B) 0
C) 0.50
D) cannot be determined from the information given

Question 35

TABLE 4-1
Mothers Against Drunk Driving is a very visible group whose main focus is to educate the public about the harm caused by drunk drivers. A study was recently done that emphasized the problem we all face with drinking and driving. Four hundred accidents that occurred on a Saturday night were analyzed. Two items noted were the number of vehicles involved and whether alcohol played a role in the accident. The numbers are shown below:
$$\begin{array}{l}\text { Number of Vehicles Involved }\\\begin{array} { l c c c c } \text { Did alcohol play a role? } & 1 & 2 & 3 & \text { Totals } \\\hline \text { Yes } & 50 & 100 & 20 & 170 \\\hline \text { No } & 25 & 175 & 30 & 230 \\\text { Totals } & 75 & 275 & 50 & 400 \\\hline\end{array}\end{array}$$

-Referring to Table 4-1, given that alcohol was not involved, what proportion of the accidents were multiple vehicle?

A) 120/170 or 70.59%
B) 50/170 or 29.41%
C) 205/230 or 89.13%
D) 25/230 or 10.87%

Question 36

If events A and B are mutually exclusive and collectively exhaustive, what is the probability that event A occurs?

A) 1.00
B) 0
C) 0.50
D) cannot be determined from the information given

Question 37

TABLE 4-1
Mothers Against Drunk Driving is a very visible group whose main focus is to educate the public about the harm caused by drunk drivers. A study was recently done that emphasized the problem we all face with drinking and driving. Four hundred accidents that occurred on a Saturday night were analyzed. Two items noted were the number of vehicles involved and whether alcohol played a role in the accident. The numbers are shown below:
$$\begin{array}{l}\text { Number of Vehicles Involved }\\\begin{array} { l c c c c c } { \text { Did alcohol playa role? } } & 1 & 2 & 3 & \text { Totals } \\\hline \text { Yes } & 50 & 100 & 20 & 170 \\\hline \text { No } & 25 & 175 & 30 & 230 \\\text { Totals } & 75 & 275 & 50 & 400 \\\hline\end{array}\end{array}$$

-Referring to Table 4-1, given that multiple vehicles were involved, what proportion of accidents involved alcohol?

A) 120/400 or 30%
B) 120/170 or 70.59%
C) 120/325 or 36.92%
D) 120/230 or 52.17%

Question 38

The employees of a company were surveyed on questions regarding their educational background and marital status. Of the 600 employees, 400 had college degrees, 100 were single, and 60 were single college graduates. What is the probability that an employee of the company is single or has a college degree?

A) 0.25
B) 0.733
C) 0.10
D) 0.667

Question 39

The probability that a new advertising campaign will increase sales is assessed as being 0.80. The probability that the cost of developing the new ad campaign can be kept within the original budget allocation is 0.40. Assuming that the two events are independent, what is the probability that the cost is not kept within budget or the campaign will not increase sales?

A) 0.68
B) 0.32
C) 0.12
D) 0.88

Question 40

A company has 2 machines that produce widgets. An older machine produces 23% defective widgets, while the new machine produces only 8% defective widgets. In addition, the new machine produces 3 times as many widgets as the older machine does. What is the probability that a randomly chosen widget produced by the company is defective?

A) 0.078
B) 0.156
C) 0.1175
D) 0.310

Question 41

Simple probability is also called

A) Bayes' theorem.
B) joint probability.
C) conditional probability.
D) marginal probability.

Question 42

If two equally likely events A and B are mutually exclusive, what is the probability that event A occurs?

A) 1.00
B) 0
C) 0.50
D) cannot be determined from the information given

Question 43

If two equally likely events A and B are mutually exclusive and collectively exhaustive, what is the probability that event A occurs?
A) 0

A) 1.00
B) 0.50
B) cannot be determined from the information given

Question 44

The probability that house sales will increase in the next 6 months is estimated to be 0.25. The probability that the interest rates on housing loans will go up in the same period is estimated to be 0.74. The probability that house sales or interest rates will go up during the next 6 months is estimated to be 0.89. What is the probability that both house sales and interest rates will increase during the next 6 months?

A) 0.90
B) 0.10
C) 0.705
D) 0.185

Question 45

$$\text { TABLE 4-2 }$$ An alcoholawareness task force at a Big-Ten universitysampled 200 studentsafter the midterm toask them whether they went barhopping the weekend before the midterm orspent the weekend studying,and whetherthey did well or poorly on the midterm. The following result was obtained.

$\begin{array}{l|cc} & \text {Did Well on Midterm }&\text { Did Poorly on Midterm} \\\hline \text {Studying for Exam }& 80 & 20 \\\text {Went Bar Hopping }& 30 & 70\end{array}$


-Referring to Table 4-2, what is the probability that a randomly selected student who went bar hopping will do well on the midterm?

A) 30/200 or 15%
B) 30/110 or 27.27%
C) (100/200) × (110/200) or 27.50%
D) 30/100 or 30%

Question 46

When using the general multiplication rule, P(A and

A) P(B)/P(A).
B) P(A|B)P(B).
B) is equal to
C) P(A)P(B).
D) P(A)/P(B).

Question 47

If two events are mutually exclusive and collectively exhaustive, what is the probability that both occur?

A) 1.00
B) 0
C) 0.50
D) cannot be determined from the information given

Question 48

A company has 2 machines that produce widgets. An older machine produces 23% defective widgets, while the new machine produces only 8% defective widgets. In addition, the new machine produces 3 times as many widgets as the older machine does. Given that a widget was produced by the new machine, what is the probability it is not defective?

A) 0.06
B) 0.50
C) 0.94
D) 0.92

Question 49

Selection of raffle tickets from a large bowl is an example of

A) subjective probability.
B) sampling without replacement.
C) sampling with replacement.
D) none of the above

Question 50

According to a survey of American households, the probability that the residents own 2 cars if annual household income is over $25,000 is 80%. Of the households surveyed, 60% had incomes over $25,000 and 70% had 2 cars. What is the probability that annual household income is over $25,000 if the residents of a household do not own 2 cars?

A) 0.12
B) 0.18
C) 0.70
D) 0.40

Question 51

TABLE 4-2
An alcohol awareness task force at a Big-Ten university sampled 200 students after the midterm to ask them whether they went bar hopping the weekend before the midterm or spent the weekend studying, and whether they did well or poorly on the midterm. The following result was obtained.

$\begin{array}{l|cc} & \text {Did Well on Midterm} & \text {Did Poorly on Midterm} \\\hline\text {Studying for Exam }& 80 & 20 \\\text {Went Bar Hopping} & 30 & 70\end{array}$


-Referring to Table 4-2, the events "Did Well on Midterm" and "Studying for Exam" are

A) not statistically dependent.
B) collective exhaustive.
C) not mutually exclusive.
D) none of the above

Question 52

According to a survey of American households, the probability that the residents own 2 cars if annual household income is over $25,000 is 80%. Of the households surveyed, 60% had incomes over $25,000 and 70% had 2 cars. What is the probability that the residents of a household own 2 cars and have an income less than or equal to $25,000 a year?

A) 0.22
B) 0.48
C) 0.12
D) 0.18

Question 53

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. TABLE 4-3
A survey is taken among customers of a fast-food restaurant to determine preference for hamburger or chicken. Of 200 respondents selected, 75 were children and 125 were adults. 120 preferred hamburger and 80 preferred chicken. 55 of the children preferred hamburger.

-Referring to Table 4-3, the probability that a randomly selected individual is an adult is________

Question 54

TABLE 4-2
An alcohol awareness task force at a Big-Ten university sampled 200 students after the midterm to ask them whether they went bar hopping the weekend before the midterm or spent the weekend studying, and whether they did well or poorly on the midterm. The following result was obtained.

$\begin{array}{l|cc} & \text {Did Well on Midterm} & \text {Did Poorly on Midterm} \\\hline\text {Studying for Exam }& 80 & 20 \\\text {Went Bar Hopping} & 30 & 70\end{array}$


-Referring to Table 4-2, the events "Did Well on Midterm" and "Did Poorly on Midterm" are

A) collective exhaustive.
B) statistically dependent.
C) mutually exclusive.
D) all of the above

Question 55

TABLE 4-2
An alcohol awareness task force at a Big-Ten university sampled 200 students after the midterm to ask them whether they went bar hopping the weekend before the midterm or spent the weekend studying, and whether they did well or poorly on the midterm. The following result was obtained.

$\begin{array}{l|cc} & \text {Did Well on Midterm} & \text {Did Poorly on Midterm} \\\hline\text {Studying for Exam }& 80 & 20 \\\text {Went Bar Hopping} & 30 & 70\end{array}$


-Referring to Table 4-1, given that 3 vehicles were involved, what proportion of accidents involved alcohol?

A) 20/50 or 40%
B) 20/170 or 11.77%
C) 20/400 or 5%
D) 20/30 or 66.67%

Question 56

$$\text { TABLE 4-2 }$$ An alcohol awareness task force at a Big-Ten university sampled 200 students after the midterm to ask them whether they went bar hopping the weekend before the midterm or spent the weekend studying, and whether they did well or poorly on the midterm. The following result was obtained.
$$\begin{array}{l}\begin{array} { lcc} &\text { Did Well on Midterm}& \text {Did Poorlyon Midterm }\\\hline \text { Studyingror Exam } & 80 & 20 \\\text { Went Bar Hopping } & 30 & 70\end{array}\end{array}$$


-Referring to Table 4-2, what is the probability that a randomly selected student did well on the midterm and also went bar hopping the weekend before the midterm?

A) (80 + 30)/200 or 55%
B) 30/200 or 15%
C) (80 + 30 + 70)/200 or 90%
D) (30 + 70)/200 or 50%

Question 57

The closing price of a company's stock tomorrow can be lower, higher or the same as today's closed. Without any prior information that may affect the price of the stock tomorrow, the probability that it will close higher than today's close is 1/3. This is an example of using which of the following probability approach?

A) subjective probability
B) a priori classical probability
C) empirical classical probability
D) conditional probability

Question 58

If two events are mutually exclusive, what is the probability that one or the other occurs?

A) 0.50
B) 0
C) 1.00
D) cannot be determined from the information given

Question 59

According to a survey of American households, the probability that the residents own 2 cars if annual household income is over $25,000 is 80%. Of the households surveyed, 60% had incomes over $25,000 and 70% had 2 cars. What is the probability that the residents of a household own 2 cars and have an income over $25,000 a year?

A) 0.18
B) 0.22
C) 0.48
D) 0.12

Question 60

TABLE 4-1
Mothers Against Drunk Driving is a very visible group whose main focus is to educate the public about the harm caused by drunk drivers. A study was recently done that emphasized the problem we all face with drinking and driving. Four hundred accidents that occurred on a Saturday night were analyzed. Two items noted were the number of vehicles involved and whether alcohol played a role in the accident. The numbers are shown below:
$$\begin{array}{l}\text { Number of Vehicles Involved }\\\begin{array} { l c c c c } \text { Did alcohol playa role? } & 1 & 2 & 3 & \text { Totals } \\\hline \text { Yes } & 50 & 100 & 20 & 170 \\\hline \text { No } & 25 & 175 & 30 & 230 \\\text { Totals } & 75 & 275 & 50 & 400 \\\hline\end{array}\end{array}$$

-Referring to Table 4-1, what proportion of accidents involved alcohol and a single vehicle?

A) 50/400 or 12.5%
B) 25/400 or 6.25%
C) 195/400 or 48.75%
D) 245/400 or 61.25%

Question 61

TABLE 4-3
A survey is taken among customers of a fast-food restaurant to determine preference for hamburger or chicken. Of 200 respondents selected, 75 were children and 125 were adults. 120 preferred hamburger and 80 preferred chicken. 55 of the children preferred hamburger.

-Referring to Table 4-3, assume we know the person is a child. The probability that this individual prefers hamburger is ______.

Question 62

A debate team of 4 is to be chosen from a class of 35. There are two twin brothers in the class. How many possible ways can the team be formed which will include both of the twin brothers?

Question 63

TABLE 4-4
Suppose that patrons of a restaurant were asked whether they preferred beer or whether they preferred wine. 70% said that they preferred beer. 60% of the patrons were male. 80% of the males preferred beer.

-Referring to Table 4-4, suppose a randomly selected patron prefers beer. Then the probability the patron is a male is _______.

Question 64

TABLE 4-5
In a meat packaging plant Machine A accounts for 60% of the plant's output, while Machine B accounts for 40% of the plant's output. In total, 4% of the packages are improperly sealed. Also, 3% of the packages are from Machine A and are improperly sealed.

-Referring to Table 4-5, if a package selected at random is improperly sealed, the probability that it came from machine A is_______ .

Question 65

TABLE 4-8
According to the record of the registrar's office at a state university, 35% of the students are freshman, 25% are sophomore, 16% are junior and the rest are senior. Among the freshmen, sophomores, juniors and seniors, the portion of students who live in the dormitory are, respectively, 80%, 60%, 30% and 20%.
Referring to Table 4-8, if a randomly selected student does not live in the dormitory, what is the probability that the student is a junior or a senior?

Question 66

An exploration team of 2 women and 3 men is to be chosen from a candidate pool of 6 women and 7 men. How many different ways can this team of 5 be formed?

Question 67

TABLE 4-4
Suppose that patrons of a restaurant were asked whether they preferred beer or whether they preferred wine. 70% said that they preferred beer. 60% of the patrons were male. 80% of the males preferred beer.

-Referring to Table 4-4, the probability a randomly selected patron prefers wine is_____.

Question 68

Suppose A and B are events where P(A) = 0.4, P(B) = 0.5, and P(A andB) = 0.1. Then P(B|A)= _______.

Question 69

A survey conducted by the Segal Company of New York found that in a sample of 189 large companies, 40 offered stock options to their board members as part of their non-cash compensation packages. For small- to mid-sized companies, 43 of the 180 surveyed indicated that they offer stock options as part of their noncash compensation packages to their board members.
Referring to Table 4-9, if a randomly selected company is a large company, what is the probability that it offered stock options to their board members?

Question 70

TABLE 4-5
In a meat packaging plant Machine A accounts for 60% of the plant's output, while Machine B accounts for 40% of the plant's output. In total, 4% of the packages are improperly sealed. Also, 3% of the packages are from Machine A and are improperly sealed.

-Referring to Table 4-5, if a package selected at random came from Machine B, the probability that it is properly sealed is _______.

Question 71

TABLE 4-5
In a meat packaging plant Machine A accounts for 60% of the plant's output, while Machine B accounts for 40% of the plant's output. In total, 4% of the packages are improperly sealed. Also, 3% of the packages are from Machine A and are improperly sealed.

-Referring to Table 4-5, if a package selected at random came from Machine B, the probability that it is improperly sealed is ______.

Question 72

TABLE 4-9
A survey conducted by the Segal Company of New York found that in a sample of 189 large companies, 40 offered stock options to their board members as part of their non-cash compensation packages. For small- to mid-sized companies, 43 of the 180 surveyed indicated that they offer stock options as part of their noncash compensation packages to their board members.
Referring to Table 4-9, is the size of the company statistically independent of whether stock options are offered to their board members and why?

Question 73

TABLE 4-8
According to the record of the registrar's office at a state university, 35% of the students are freshman, 25% are sophomore, 16% are junior and the rest are senior. Among the freshmen, sophomores, juniors and seniors, the portion of students who live in the dormitory are, respectively, 80%, 60%, 30% and 20%.
Referring to Table 4-8, what percentage of the students live in a dormitory?

Question 74

Are whites more likely to claim bias? It was found that 60% of the workers were white, 30% were black and 10% are other races. Given that a worker was white, the probability that the worker had claimed bias was 30%. Given that a worker was black, the probability that the worker had claimed bias was 40%. Given that a worker was other race, the probability that the worker had claimed bias was 0%.
Referring to Table 4-10, if a randomly selected worker had not claimed bias, what is the probability that the worker is white?

Question 75

TABLE 4-6
At a Texas college, 60% of the students are from the southern part of the state, 30% are from the northern part of the state, and the remaining 10% are from out-of-state. All students must take and pass an Entry Level Math (ELM) test. 60% of the southerners have passed the ELM, 70% of the northerners have passed the ELM, and 90% of the out-of-staters have passed the ELM.

-Referring to Table 4-6, the probability that a randomly selected student is not from southern Texas and has not passed the ELM is _______.

Question 76

Suppose A and B are independent events where P(A) = 0.4 and P(B) = 0.5. Then P(A andB) =____

Question 77

At the International Pancakes Hut, there are 4 different ways to have an egg cooked, 7 different choices of pancakes, 5 different types of syrups and 8 different beverages. How many different ways are there to order an egg, a pancake with a choice of syrup and a beverage?

Question 78

TABLE 4-9
A survey conducted by the Segal Company of New York found that in a sample of 189 large companies, 40 offered stock options to their board members as part of their non-cash compensation packages. For small- to mid-sized companies, 43 of the 180 surveyed indicated that they offer stock options as part of their noncash compensation packages to their board members.
Referring to Table 4-9, if a randomly selected company offered stock options to their board member, what is the probability that it is a large company?

Question 79

Suppose A and B are events where P(A) = 0.4, P(B) = 0.5, and P(A andB) = 0.1. Then P(A|B)= ______.

Question 80

Eleven freshmen are to be assigned to eleven empty rooms in a student dormitory. Each room is considered unique so that it matters who is being assigned to which room. How many different ways can those eleven freshmen be allocated?