Deck 6: Probability

Question 1

Sports Fans
Suppose that past history shows that 5% of college students are sports fans.A sample of 10 students is to be selected.
The relative frequency approach to probability uses long term relative frequencies,often based on past data.

Answer 1

True

Question 2

P(A)+ P(B)= 1 for any events A and B that are mutually exclusive.

Answer 2

False

Question 3

An approach of assigning probabilities which assumes that all outcomes of the experiment are equally likely is referred to as the:

A) subjective approach
B) objective approach
C) classical approach
D) relative frequency approach

Answer 3

C

Question 4

If an experiment consists of five outcomes with P(O₁)= 0.10,P(O₂)= 0.20,P(O₃)= 0.30,P(O₄)= 0.25,then P(O₅)is

A) 0.75
B) 0.15
C) 0.50
D) Cannot be determined from the information given.

Question 5

The collection of all possible outcomes of an experiment is called:

A) a simple event
B) a sample space
C) a sample
D) a population

Question 6

Which of the following is an approach to assigning probabilities?

A) Classical approach
B) Relative frequency approach
C) Subjective approach
D) All of these choices are true.

Question 7

The collection of all the possible outcomes of a random experiment is called a sample space.

Question 8

If either event A or event B must occur,then A and B are mutually exclusive and collectively exhaustive events.

Question 9

Sports Fans
Suppose that past history shows that 5% of college students are sports fans.A sample of 10 students is to be selected.
Predicting the outcome of a football game is using the subjective approach to probability.

Question 10

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

Question 11

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

Question 12

You think you have a 90% chance of passing your next advanced financial accounting exam.This is an example of subjective approach to probability.

Question 13

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

Question 14

If either event A or event B must occur,they are called mutually exclusive.

Question 15

If A and B are mutually exclusive events with P(A)= 0.75,then P(B):

A) can be any value between 0 and 1.
B) can be any value between 0 and 0.75.
C) cannot be larger than 0.25.
D) equals 0.25.

Question 16

A sample space of an experiment consists of the following outcomes: 1,2,3,4,and 5.Which of the following is a simple event?

A) At least 3
B) At most 2
C) 3
D) 15

Question 17

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

A) 0.00
B) 0.50
C) 1.00
D) Cannot be determined from the information given.

Question 18

If you roll a balanced die 50 times,you should expect an even number to appear:

A) on every other roll.
B) exactly 50 times out of 100 rolls.
C) 25 times on average,over the long term.
D) All of these choices are true.

Question 19

Of the last 500 customers entering a supermarket,50 have purchased a wireless phone.If the relative frequency approach for assigning probabilities is used,the probability that the next customer will purchase a wireless phone is

A) 0.10
B) 0.90
C) 0.50
D) None of these choices.

Question 20

Which of the following is a requirement of the probabilities assigned to outcome O_i?

A) P(O_i) $\le$ 0 for each i
B) P(O_i) $\ge$ 1 for each i
C) 0 $\le$ P(O_i) $\le$ 1 for each i
D) P(O_i)= 1 for each i

Question 21

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

A) 0.00
B) 0.50
C) 1.00
D) Cannot be determined from the information given.

Question 22

No matter which approach was used to assign probability (classical,relative frequency,or subjective)the one that is always used to interpret a probability is the ____________________ approach.

Question 23

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

A) 0.00
B) 0.50
C) 1.00
D) Cannot be determined from the information given.

Question 24

There are ____________________ requirements of probabilities for the outcomes of a sample space.

Question 25

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

A) mutually exclusive
B) independent
C) collectively exhaustive
D) None of these choices.

Question 26

An individual outcome of a sample space is called a(n)____________________ event.

Question 27

The outcomes of a sample space must be ____________________,which means that all possible outcomes must be included.

Question 28

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

A) 0.00
B) 0.50
C) 1.00
D) Cannot be determined from the information given.

Question 29

The probability of an event is the ____________________ of the probabilities of the simple events that constitute the event.

Question 30

A(n)____________________ of a random experiment is a list of all possible outcomes of the experiment.

Question 31

The outcomes of a sample space must be ____________________ and ____________________.

Question 32

A(n)____________________ is a collection or set of one or more simple events in a sample space.

Question 33

Hobby Shop Sales
Sales records of a hobby shop showed the following number of radio controlled trucks sold weekly for each of the last 50 weeks.

{Hobby Shop Sales Narrative} Define the random experiment of interest to the store.

Question 34

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

A) 0.00
B) 0.50
C) 1.00
D) Cannot be determined from the information given.

Question 35

The collection of all possible events is called

A) an outcome
B) a sample space
C) an event
D) None of these choices.

Question 36

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

A) 0.00
B) 0.50
C) 1.00
D) Cannot be determined from the information given.

Question 37

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

A) 0.00
B) 0.50
C) 1.00
D) Cannot be determined from the information given.

Question 38

A random experiment is an action or process that leads to one of several possible ____________________.

Question 39

The outcomes of a sample space must be ____________________,which means that no two outcomes can occur at the same time.

Question 40

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

A) 0.25
B) 0.50
C) 1.00
D) Cannot be determined from the information given.

Question 41

Equity Loan Rates
A survey of banks estimated the following probabilities for the interest rate being charged on a equity loan based on a 30-year loan,based on past records.
$$\begin{array} { | l | c c c c c | } \hline \text { Interest Rate } & 0.0 \% & 6.5 \% & 7.0 \% & 7.5 \% & > 7.5 \% \\\hline \text { Probability } & 0.20 & 0.23 & 0.25 & 0.28 & .04 \\\hline\end{array}$$

-Two events A and B are independent if P(A and B)= 0.

Question 42

Equity Loan Rates
A survey of banks estimated the following probabilities for the interest rate being charged on a equity loan based on a 30-year loan,based on past records.
$$\begin{array} { | l | c c c c c | } \hline \text { Interest Rate } & 0.0 \% & 6.5 \% & 7.0 \% & 7.5 \% & > 7.5 \% \\\hline \text { Probability } & 0.20 & 0.23 & 0.25 & 0.28 & .04 \\\hline\end{array}$$

-The probability of the intersection is called a joint probability.

Question 43

Equity Loan Rates
A survey of banks estimated the following probabilities for the interest rate being charged on a equity loan based on a 30-year loan,based on past records.

{Equity Loan Rates Narrative} If a bank is selected at random from this distribution,what is the probability that the interest rate charged on a home loan exceeds 7.0%?

Question 44

Equity Loan Rates
A survey of banks estimated the following probabilities for the interest rate being charged on a equity loan based on a 30-year loan,based on past records.
$$\begin{array} { | l | c c c c c | } \hline \text { Interest Rate } & 0.0 \% & 6.5 \% & 7.0 \% & 7.5 \% & > 7.5 \% \\\hline \text { Probability } & 0.20 & 0.23 & 0.25 & 0.28 & .04 \\\hline\end{array}$$

-If A and B are independent events with P(A)= .40 and P(B)= .50,then P(A and B)= .20.

Question 45

Hobby Shop Sales
Sales records of a hobby shop showed the following number of radio controlled trucks sold weekly for each of the last 50 weeks.

{Hobby Shop Sales Narrative} What is the probability of selling between 1 and 3 (inclusive)trucks in any given week?

Question 46

Equity Loan Rates
A survey of banks estimated the following probabilities for the interest rate being charged on a equity loan based on a 30-year loan,based on past records.
$$\begin{array} { | l | c c c c c | } \hline \text { Interest Rate } & 0.0 \% & 6.5 \% & 7.0 \% & 7.5 \% & > 7.5 \% \\\hline \text { Probability } & 0.20 & 0.23 & 0.25 & 0.28 & .04 \\\hline\end{array}$$

-The intersection of two events A and B is the event that occurs when both A and B occur.

Question 47

Equity Loan Rates
A survey of banks estimated the following probabilities for the interest rate being charged on a equity loan based on a 30-year loan,based on past records.
$$\begin{array} { | l | c c c c c | } \hline \text { Interest Rate } & 0.0 \% & 6.5 \% & 7.0 \% & 7.5 \% & > 7.5 \% \\\hline \text { Probability } & 0.20 & 0.23 & 0.25 & 0.28 & .04 \\\hline\end{array}$$

-If A and B are independent,then P(A|B)= P(A)or P(B|A)= P(B).

Question 48

Equity Loan Rates
A survey of banks estimated the following probabilities for the interest rate being charged on a equity loan based on a 30-year loan,based on past records.
$$\begin{array} { | l | c c c c c | } \hline \text { Interest Rate } & 0.0 \% & 6.5 \% & 7.0 \% & 7.5 \% & > 7.5 \% \\\hline \text { Probability } & 0.20 & 0.23 & 0.25 & 0.28 & .04 \\\hline\end{array}$$

-Two or more events are said to be independent when the occurrence of one event has no effect on the probability that another will occur.

Question 49

Equity Loan Rates
A survey of banks estimated the following probabilities for the interest rate being charged on a equity loan based on a 30-year loan,based on past records.
$$\begin{array} { | l | c c c c c | } \hline \text { Interest Rate } & 0.0 \% & 6.5 \% & 7.0 \% & 7.5 \% & > 7.5 \% \\\hline \text { Probability } & 0.20 & 0.23 & 0.25 & 0.28 & .04 \\\hline\end{array}$$

-The union of events A and B is the event that occurs when either A or B or both occur.It is denoted as 'A or B'.

Question 50

Equity Loan Rates
A survey of banks estimated the following probabilities for the interest rate being charged on a equity loan based on a 30-year loan,based on past records.

{Equity Loan Rates Narrative} What approach was used in estimating the probabilities for the interest rates?

Question 51

Hobby Shop Sales
Sales records of a hobby shop showed the following number of radio controlled trucks sold weekly for each of the last 50 weeks.

{Hobby Shop Sales Narrative} What is the probability of selling at least two trucks in any given week?

Question 52

Hobby Shop Sales
Sales records of a hobby shop showed the following number of radio controlled trucks sold weekly for each of the last 50 weeks.

{Hobby Shop Sales Narrative} What approach would you use in determining the probabilities for next week's sales? Assign probabilities to the outcomes.

Question 53

Equity Loan Rates
A survey of banks estimated the following probabilities for the interest rate being charged on a equity loan based on a 30-year loan,based on past records.
$$\begin{array} { | l | c c c c c | } \hline \text { Interest Rate } & 0.0 \% & 6.5 \% & 7.0 \% & 7.5 \% & > 7.5 \% \\\hline \text { Probability } & 0.20 & 0.23 & 0.25 & 0.28 & .04 \\\hline\end{array}$$

-The conditional probability of event B given event A is denoted by P(A|B).

Question 54

Equity Loan Rates
A survey of banks estimated the following probabilities for the interest rate being charged on a equity loan based on a 30-year loan,based on past records.
$$\begin{array} { | l | c c c c c | } \hline \text { Interest Rate } & 0.0 \% & 6.5 \% & 7.0 \% & 7.5 \% & > 7.5 \% \\\hline \text { Probability } & 0.20 & 0.23 & 0.25 & 0.28 & .04 \\\hline\end{array}$$

-Two events A and B are said to be independent if P(A|B)= P(B).

Question 55

Hobby Shop Sales
Sales records of a hobby shop showed the following number of radio controlled trucks sold weekly for each of the last 50 weeks.

{Hobby Shop Sales Narrative} List the outcomes in the sample space.

Question 56

Mutual Fund Price
An investor estimates that there is a 75% chance that a particular mutual fund's price will increase to $100 per share over the next three weeks,based on past data.
{Mutual Fund Price Narrative} Which approach was used to produce this figure?

Question 57

Equity Loan Rates
A survey of banks estimated the following probabilities for the interest rate being charged on a equity loan based on a 30-year loan,based on past records.
$$\begin{array} { | l | c c c c c | } \hline \text { Interest Rate } & 0.0 \% & 6.5 \% & 7.0 \% & 7.5 \% & > 7.5 \% \\\hline \text { Probability } & 0.20 & 0.23 & 0.25 & 0.28 & .04 \\\hline\end{array}$$

-The union of events A and B is the event that occurs when either A or B occurs but not both.

Question 58

Equity Loan Rates
A survey of banks estimated the following probabilities for the interest rate being charged on a equity loan based on a 30-year loan,based on past records.

{Equity Loan Rates Narrative} What is the most common interest rate?

Question 59

Mutual Fund Price
An investor estimates that there is a 75% chance that a particular mutual fund's price will increase to $100 per share over the next three weeks,based on past data.
{Mutual Fund Price Narrative} Interpret the 75% probability.

Question 60

Equity Loan Rates
A survey of banks estimated the following probabilities for the interest rate being charged on a equity loan based on a 30-year loan,based on past records.
$$\begin{array} { | l | c c c c c | } \hline \text { Interest Rate } & 0.0 \% & 6.5 \% & 7.0 \% & 7.5 \% & > 7.5 \% \\\hline \text { Probability } & 0.20 & 0.23 & 0.25 & 0.28 & .04 \\\hline\end{array}$$

-If A and B are independent events with P(A)= 0.35 and P(B)= 0.55,then P(A|B)is 0.35/0.55 = .64.

Question 61

If A and B are disjoint events with P(A)= 0.70,then P(B):

A) can be any value between 0 and 1
B) can be any value between 0 and 0.70
C) cannot be larger than 0.30
D) cannot be determined with the information given

Question 62

Equity Loan Rates
A survey of banks estimated the following probabilities for the interest rate being charged on a equity loan based on a 30-year loan,based on past records.
$$\begin{array} { | l | c c c c c | } \hline \text { Interest Rate } & 0.0 \% & 6.5 \% & 7.0 \% & 7.5 \% & > 7.5 \% \\\hline \text { Probability } & 0.20 & 0.23 & 0.25 & 0.28 & .04 \\\hline\end{array}$$

-Suppose the probability that a person owns both a cat and a dog is 0.10.Also suppose the probability that a person owns a cat but not a dog is 0.20.The marginal probability that someone owns a cat is 0.30.

Question 63

Suppose P(A)= 0.60,P(B)= 0.85,and A and B are independent.The probability of the complement of the event (A and B)is:

A) .4 * .15 = .060
B) 0.40 + .15 = .55
C) 1 - (.40 + .15)= .45
D) 1 - (.6 * .85)= .490

Question 64

Equity Loan Rates
A survey of banks estimated the following probabilities for the interest rate being charged on a equity loan based on a 30-year loan,based on past records.
$$\begin{array} { | l | c c c c c | } \hline \text { Interest Rate } & 0.0 \% & 6.5 \% & 7.0 \% & 7.5 \% & > 7.5 \% \\\hline \text { Probability } & 0.20 & 0.23 & 0.25 & 0.28 & .04 \\\hline\end{array}$$

-The intersection of events A and B is the event that occurs when:

A) either A or B occurs but not both
B) neither A nor B occur
C) both A and B occur
D) All of these choices are true.

Question 65

A and B are disjoint events,with P(A)= 0.20 and P(B)= 0.30.Then P(A and B)is:

A) 0.50
B) 0.10
C) 0.00
D) 0.06

Question 66

Cars
Suppose X = the number of cars owned by a family in the U.S.The probability distribution of X is shown in the table below.
$\begin{array}{|l|c|c|c|c|}\hline X & 0 & 1 & 2 & 3 \\\hline \text { Probability } & 0.56 & 0.23 & 0.12 & 0.09 \\\hline\end{array}$

-{Cars Narrative} Suppose you choose two families at random.What is the chance that they each own one car? (That means family A owns a car and family B owns a car. )

A) 0.23
B) 0.23 + 0.23 = 0.46
C) 0.23 + 0.23 - (0.23)*(0.23)= .4071
D) (0.23)*(0.23)= 0.0529

Question 67

Equity Loan Rates
A survey of banks estimated the following probabilities for the interest rate being charged on a equity loan based on a 30-year loan,based on past records.
$$\begin{array} { | l | c c c c c | } \hline \text { Interest Rate } & 0.0 \% & 6.5 \% & 7.0 \% & 7.5 \% & > 7.5 \% \\\hline \text { Probability } & 0.20 & 0.23 & 0.25 & 0.28 & .04 \\\hline\end{array}$$

-The probability of event A given event B is denoted by

A) P(A and B)
B) P(A or B)
C) P(A|B)
D) P(B|A)

Question 68

Which of the following statements is correct if the events A and B have nonzero probabilities?

A) A and B cannot be both independent and disjoint
B) A and B can be both independent and disjoint
C) A and B are always independent
D) A and B are always disjoint

Question 69

Cars
Suppose X = the number of cars owned by a family in the U.S.The probability distribution of X is shown in the table below.
$\begin{array}{|l|c|c|c|c|}\hline X & 0 & 1 & 2 & 3 \\\hline \text { Probability } & 0.56 & 0.23 & 0.12 & 0.09 \\\hline\end{array}$

-{Car Narrative}What is the chance that a family owns more than one car?

A) 0.23
B) 0.21
C) 0.44
D) None of these choices.

Question 70

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 71

If P(A)= 0.35,P(B)= 0.45,and P(A and B)= 0.25,then P(A|B)is:

A) 1.4
B) 1.8
C) 0.714
D) 0.556

Question 72

If P(A)= 0.25 and P(B)= 0.65,then P(A and B)is:

A) 0.25
B) 0.40
C) 0.90
D) cannot be determined from the information given

Question 73

If A and B are independent events with P(A)= 0.20 and P(B)= 0.60,then P(A|B)is:

A) 0.20
B) 0.60
C) 0.40
D) 0.80

Question 74

Which of the following best describes the concept of marginal probability?

A) It is a measure of the likelihood that a particular event will occur,regardless of whether another event occurs.
B) It is a measure of the likelihood that a particular event will occur,if another event has already occurred.
C) It is a measure of the likelihood of the simultaneous occurrence of two or more events.
D) None of these choices.

Question 75

Equity Loan Rates
A survey of banks estimated the following probabilities for the interest rate being charged on a equity loan based on a 30-year loan,based on past records.
$$\begin{array} { | l | c c c c c | } \hline \text { Interest Rate } & 0.0 \% & 6.5 \% & 7.0 \% & 7.5 \% & > 7.5 \% \\\hline \text { Probability } & 0.20 & 0.23 & 0.25 & 0.28 & .04 \\\hline\end{array}$$

-If P(A)= .30,P(B)= .60,and P(A and B)= .20,then P(A|B)= .40.

Question 76

If A and B are independent events with P(A)= 0.60 and P(A|B)= 0.60,then P(B)is:

A) 1.20
B) 0.60
C) 0.36
D) cannot be determined with the information given

Question 77

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 these choices.

Question 78

Equity Loan Rates
A survey of banks estimated the following probabilities for the interest rate being charged on a equity loan based on a 30-year loan,based on past records.
$$\begin{array} { | l | c c c c c | } \hline \text { Interest Rate } & 0.0 \% & 6.5 \% & 7.0 \% & 7.5 \% & > 7.5 \% \\\hline \text { Probability } & 0.20 & 0.23 & 0.25 & 0.28 & .04 \\\hline\end{array}$$

-The probability of the intersection of two events A and B is denoted by P(A and B)and is called the:

A) marginal probability
B) joint probability
C) conditional probability of A given B
D) conditional probability of B given A

Question 79

Which of the following is equivalent to P(A|B)?

A) P(A and B)
B) P(B|A)
C) P(A)/P(B)
D) None of these choices.

Question 80

If P(A)= 0.65,P(B)= 0.58,and P(A and B)= 0.76,then P(A or B)is:

A) 1.23
B) 0.47
C) 0.18
D) 0.11