Deck 4: Basic Probability

Question 1

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

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

Answer 1

collectively exhaustive.

Question 2

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

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

Answer 2

cannot be determined from the information given

Question 3

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) independent.
C) collectively exhaustive.
D) none of the above

Answer 3

mutually exclusive.

Question 4

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

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

Question 5

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

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

Question 6

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

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

Question 7

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

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

Question 8

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

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

Question 9

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

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

Question 10

When using the general multiplication rule, P(A and B)is equal to

A) P(A|B)P(B).
B) P(A)P(B).
C) P(B)/P(A).
D) P(A)/P(B).

Question 11

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

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

Question 12

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

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

Question 13

The collection of all possible events is called

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

Question 14

Simple probability is also called

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

Question 15

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

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

Question 16

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

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

Question 17

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

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

Question 18

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

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

Question 19

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

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

Question 20

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

Question 21

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, the probability that the cost is kept within budget and the campaign will increase sales is ________.

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

Question 22

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. The probability that both house sales and interest rates will increase during the next 6 months is ________.

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

Question 23

According to a survey of American households, the probability that the residents own two cars if annual household income is over $50,000 is 80%. Of the households surveyed, 60% had incomes over $50,000 and 70% had two cars. The probability that the residents of a household own two cars and have an income over $50,000 a year is ________.

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

Question 24

According to a survey of American households, the probability that the residents own two cars if annual household income is over $50,000 is 80%. Of the households surveyed, 60% had incomes over $50,000 and 70% had two cars. The probability that annual household income is over $50,000 if the residents of a household own two cars is ________.

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

Question 25

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, the probability that the cost is not kept within budget or the campaign will not increase sales is ________.

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

Question 26

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, the probability that neither the cost is kept within budget nor the campaign will increase sales is ________.

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

Question 27

According to a survey of American households, the probability that the residents own two cars if annual household income is over $50,000 is 80%. Of the households surveyed, 60% had incomes over $50,000 and 70% had two cars. The probability that annual household income is over $50,000 if the residents of a household do not own two cars is ________.

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

Question 28

The employees of a company were surveyed on questions regarding their educational background (college degree or no college degree)and marital status (single or married). Of the 600 employees, 400 had college degrees, 100 were single, and 60 were single college graduates. The probability that an employee of the company is single or has a college degree is ________.

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

Question 29

According to a survey of American households, the probability that the residents own two cars if annual household income is over $50,000 is 80%. Of the households surveyed, 60% had incomes over $50,000 and 70% had two cars. The probability that the residents of a household do not own two cars and have an income over $50,000 a year is ________.

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

Question 30

A 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 5.19%?

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

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. The events "increase in house sales" and "increase in interest rates in the next 6 months" are

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

Question 32

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. The events "increase in house sales" and "no increase in house sales in the next 6 months" are

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

Question 33

A company has two 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 three 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) 0.92
D) 0.94

Question 34

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. The probability that house sales will increase but interest rates will not increase during the next 6 months is ________.

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

Question 35

The employees of a company were surveyed on questions regarding their educational background (college degree or no college degree)and marital status (single or married). Of the 600 employees, 400 had college degrees, 100 were single, and 60 were single college graduates. The probability that an employee of the company is married and has a college degree is ________.

A) 0.0667
B) 0.567
C) 0.667
D) 0.833

Question 36

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, the probability that the cost is kept within budget or the campaign will increase sales is ________.

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

Question 37

According to a survey of American households, the probability that the residents own two cars if annual household income is over $50,000 is 80%. Of the households surveyed, 60% had incomes over $50,000 and 70% had two cars. The probability that the residents of a household own two cars and have an income less than or equal to $50,000 a year is ________.

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

Question 38

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. The probability that neither house sales nor interest rates will increase during the next 6 months is ________.

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

Question 39

According to a survey of American households, the probability that the residents own two cars if annual household income is over $50,000 is 80%. Of the households surveyed, 60% had incomes over $50,000 and 70% had two cars. The probability that the residents do not own two cars if annual household income is not over $50,000 is ________.

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

Question 40

The employees of a company were surveyed on questions regarding their educational background (college degree or no college degree)and marital status (single or married). Of the 600 employees, 400 had college degrees, 100 were single, and 60 were single college graduates. The probability that an employee of the company does not have a college degree is ________.

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

Question 41

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:

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

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

Question 42

A company has two 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 three 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) 0.1175
C) 0.156
D) 0.310

Question 43

If A and B cannot occur at the same time the events are called mutually exclusive.

Question 44

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:

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

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

Question 45

A company has two 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 three 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) 0.08
B) 0.15
C) 0.489
D) 0.511

Question 46

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.

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) (80+30)/200 or (30+80)/200 or 55%
C) (30+70)/200 or (70+30)/200 or 50%
D) (80+30+70)/200 or (110+100-30)/200 or 90%

Question 47

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:

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

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

Question 48

If either A or B must occur the events are called mutually exclusive.

Question 49

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:

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

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

Question 50

When A and B are mutually exclusive, P(A or
B) can be found by adding P(A) and P(B).

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.

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

Question 52

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.

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

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

Question 53

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.

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

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

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.

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

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

Question 55

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:

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

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

Question 56

The collection of all the possible events is called a sample space.

Question 57

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:

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

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

Question 58

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:

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

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

Question 59

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:

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

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

Question 60

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.

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

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

Question 61

TABLE 4-3
A survey is taken among customers of a fast-food restaurant to determine their 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 62

If P(A and B)= 0, then A and B must be collectively exhaustive.

Question 63

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

Question 64

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

Question 65

Suppose A and B are mutually exclusive events where P(A)= 0.4 and P(B)= 0.5. Then P(A or B)= ________.

Question 66

If P(A and B)= 1, then A and B must be collectively exhaustive.

Question 67

TABLE 4-3
A survey is taken among customers of a fast-food restaurant to determine their 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 and prefers chicken is ________.

Question 68

If P(A and B)= 0, then A and B must be mutually exclusive.

Question 69

TABLE 4-3
A survey is taken among customers of a fast-food restaurant to determine their 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 or a child is ________.

Question 70

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

Question 71

Suppose A and B are events where P(A)= 0.4, P(B)= 0.5, and P(A and B)= 0.1. Then P(A or B)= ________.

Question 72

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

Question 73

If either A or B must occur the events are called collectively exhaustive.

Question 74

If P(A and B)= 1, then A and B must be mutually exclusive.

Question 75

TABLE 4-3
A survey is taken among customers of a fast-food restaurant to determine their 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 a child and prefers chicken is ________.

Question 76

If P(A or B)= 1.0, then A and B must be mutually exclusive.

Question 77

Suppose A and B are mutually exclusive events where P(A)= 0.4 and P(B)= 0.5. Then P(A and B)= ________.

Question 78

If P(A)= 0.4 and P(B)= 0.6, then A and B must be collectively exhaustive.

Question 79

If P(A)= 0.4 and P(B)= 0.6, then A and B must be mutually exclusive.

Question 80

If P(A or B)= 1.0, then A and B must be collectively exhaustive.