Deck 6: Probability

Question 1

If joint, marginal, and conditional probabilities are available, only joint probabilities can be used to determine whether two events are dependent or independent.

Answer 1

False

Question 2

A posterior probability value is a prior probability value that has been:

A)modified on the basis of new information.
B)multiplied by a conditional probability value.
C)divided by a conditional probability value.
D)added to a conditional probability value.

Answer 2

modified on the basis of new information.

Question 3

In applying Bayes' Law, as the prior probabilities increase, the posterior probabilities decrease.

Answer 3

False

Question 4

Posterior probability of an event is the revised probability of the event after new information is available.

Question 5

Conditional probabilities are also called likelihood probabilities.

Question 6

We can apply the multiplication rule to compute the probability that two events occur at the same time.

Question 7

Prior probability of an event is the probability of the event before any information affecting it is given.

Question 8

Which of the following statements is false?

A)Thomas Bayes first employed the calculation of conditional probability in the eighteenth century.
B)There is no formula defining Bayes' Law.
C)We use a probability tree to conduct all necessary calculations for Bayes' Law.
D)None of these choices.

Question 9

Bayes' Law can be used to calculate posterior probabilities, prior probabilities, as well as new conditional probabilities.

Question 10

Posterior probabilities can be calculated using the addition rule for mutually exclusive events.

Question 11

In general, a posterior probability is calculated by adding the prior and likelihood probabilities.

Question 12

We can use the joint and marginal probabilities to compute conditional probabilities, for which a formula is available.

Question 13

Although there is a formula defining Bayes' law, you can also use a probability tree to conduct calculations.

Question 14

Bayes' Law says that P(A|B) = P(B|A)P(A).

Question 15

In problems where the joint probabilities are given, we can compute marginal probabilities by adding across rows and down columns.

Question 16

Bayes' Law is a formula for revising an initial subjective (prior) probability value on the basis of new results, thus obtaining a new (posterior) probability value.

Question 17

Prior probability is also called likelihood probability.

Question 18

Suppose we have two events A and B. We can apply the addition rule to compute the probability that at least one of these events occurs.

Question 19

Prior probabilities can be calculated using the multiplication rule for mutually exclusive events.

Question 20

Bayes' Law allows us to compute conditional probabilities from other forms of probability.

Question 21

Bayes' Law is used to compute:

A)prior probabilities.
B)joint probabilities.
C)union probabilities.
D)posterior probabilities.

Question 22

NARRBEGIN: Cysts
Cysts
After researching cysts of a particular type, a doctor learns that out of 10,000 such cysts examined, 1,500 are malignant and 8,500 are benign. A diagnostic test is available which is accurate 80% of the time (whether the cyst is malignant or not). The doctor has discovered the same type of cyst in a patient.NARREND

-{Cysts Narrative} What is the probability that the patient has a malignant cyst if he or she tests negative?

Question 23

There are situations where we witness a particular event and we need to compute the probability of one of its possible causes. ____________________ is the technique we use to do this.

Question 24

NARRBEGIN: Cysts
Cysts
After researching cysts of a particular type, a doctor learns that out of 10,000 such cysts examined, 1,500 are malignant and 8,500 are benign. A diagnostic test is available which is accurate 80% of the time (whether the cyst is malignant or not). The doctor has discovered the same type of cyst in a patient.NARREND
{Cysts Narrative} In the absence of any test, what is the probability that the cyst is benign?

Question 25

NARRBEGIN: CertificationTest
Certification Test
A standard certification test was given at three locations. 1,000 candidates took the test at location A, 600 candidates at location B, and 400 candidates at location C. The percentages of candidates from locations A, B, and C who passed the test were 70%, 68%, and 77%, respectively. One candidate is selected at random from among those who took the test.NARREND
{Certification Test Narrative} If the selected candidate passed the test, what is the probability that the candidate took the test at location B?

Question 26

Bayes' Law involves three different types of probabilities: 1) prior probabilities; 2) ____________________ probabilities; and 3) posterior probabilities.

Question 27

NARRBEGIN: CertificationTest
Certification Test
A standard certification test was given at three locations. 1,000 candidates took the test at location A, 600 candidates at location B, and 400 candidates at location C. The percentages of candidates from locations A, B, and C who passed the test were 70%, 68%, and 77%, respectively. One candidate is selected at random from among those who took the test.NARREND
{Certification Test Narrative} What is the probability that the selected candidate passed the test?

Question 28

Which of the following statements is false regarding a scenario using Bayes' Law?

A)Prior probabilities are called likelihood probabilities.
B)Conditional probabilities are called posterior probabilities.
C)Posterior probabilities are calculated by using prior probabilities that have been modified based on new information.
D)None of these choices.

Question 29

NARRBEGIN: Cysts
Cysts
After researching cysts of a particular type, a doctor learns that out of 10,000 such cysts examined, 1,500 are malignant and 8,500 are benign. A diagnostic test is available which is accurate 80% of the time (whether the cyst is malignant or not). The doctor has discovered the same type of cyst in a patient.NARREND
{Cysts Narrative} What is the probability that the patient has a benign tumor if he or she tests positive?

Question 30

Initial estimates of the probabilities of events are known as:

A)joint probabilities
B)posterior probabilities
C)prior probabilities
D)conditional probabilities

Question 31

____________________ can find the probability that someone with a disease tests positive by using (among other things) the probability that someone who actually has the disease tests positive for it.

Question 32

In the scenario of Bayes' Law, P(A|B) is a(n) ____________________ probability, while P(B|A) is a posterior probability.

Question 33

Bayes' Law involves three different types of probabilities: 1) prior probabilities; 2) likelihood probabilities; and 3) ____________________ probabilities.

Question 34

NARRBEGIN: CertificationTest
Certification Test
A standard certification test was given at three locations. 1,000 candidates took the test at location A, 600 candidates at location B, and 400 candidates at location C. The percentages of candidates from locations A, B, and C who passed the test were 70%, 68%, and 77%, respectively. One candidate is selected at random from among those who took the test.NARREND
{Certification Test Narrative} What is the probability that the selected candidate took the test at location C and failed?

Question 35

NARRBEGIN: Cysts
Cysts
After researching cysts of a particular type, a doctor learns that out of 10,000 such cysts examined, 1,500 are malignant and 8,500 are benign. A diagnostic test is available which is accurate 80% of the time (whether the cyst is malignant or not). The doctor has discovered the same type of cyst in a patient.NARREND
{Cysts Narrative} What is the probability that the patient will test negative?

Question 36

NARRBEGIN: Cysts
Cysts
After researching cysts of a particular type, a doctor learns that out of 10,000 such cysts examined, 1,500 are malignant and 8,500 are benign. A diagnostic test is available which is accurate 80% of the time (whether the cyst is malignant or not). The doctor has discovered the same type of cyst in a patient.NARREND
{Cysts Narrative} In the absence of any test, what is the probability that the cyst is malignant?

Question 37

Bayes' Law involves three different types of probabilities: 1) ____________________ probabilities; 2) likelihood probabilities; and 3) posterior probabilities.

Question 38

In the scenario of Bayes' Law, P(A|B) is a posterior probability, while P(B|A) is a(n) ____________________ probability.

Question 39

NARRBEGIN: Cysts
Cysts
After researching cysts of a particular type, a doctor learns that out of 10,000 such cysts examined, 1,500 are malignant and 8,500 are benign. A diagnostic test is available which is accurate 80% of the time (whether the cyst is malignant or not). The doctor has discovered the same type of cyst in a patient.NARREND
{Cysts Narrative} What is the probability that the patient will test positive?

Question 40

Thomas ____________________ first employed the calculation of conditional probability.

Question 41

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

Question 42

NARRBEGIN: Messenger Service
Messenger Service
Three messenger services deliver to a small town in Oregon. Service A has 60% of all the scheduled deliveries, service B has 30%, and service C has the remaining 10%. Their on-time rates are 80%, 60%, and 40% respectively. Define event O as a service delivers a package on time.NARREND
{Messenger Service Narrative} If a package was delivered on time, what is the probability that it was service A?

Question 43

NARRBEGIN: Messenger Service
Messenger Service
Three messenger services deliver to a small town in Oregon. Service A has 60% of all the scheduled deliveries, service B has 30%, and service C has the remaining 10%. Their on-time rates are 80%, 60%, and 40% respectively. Define event O as a service delivers a package on time.NARREND
{Messenger Service Narrative} Calculate the probability that a package was delivered on time.

Question 44

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

Question 45

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

Question 46

Assume that A and B are independent events with P(A) = 0.30 and P(B) = 0.50. The probability that both events will occur simultaneously is 0.80.

Question 47

NARRBEGIN: Messenger Service
Messenger Service
Three messenger services deliver to a small town in Oregon. Service A has 60% of all the scheduled deliveries, service B has 30%, and service C has the remaining 10%. Their on-time rates are 80%, 60%, and 40% respectively. Define event O as a service delivers a package on time.NARREND
{Messenger Service Narrative} Calculate P(C and O).

Question 48

If the event of interest is A, the probability that A will not occur is the complement of A.

Question 49

NARRBEGIN: Messenger Service
Messenger Service
Three messenger services deliver to a small town in Oregon. Service A has 60% of all the scheduled deliveries, service B has 30%, and service C has the remaining 10%. Their on-time rates are 80%, 60%, and 40% respectively. Define event O as a service delivers a package on time.NARREND
{Messenger Service Narrative} If a package was delivered 40 minutes late, what is the probability that it was service A?

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

If events A and B have nonzero probabilities, then they can be both independent and mutually exclusive.

Question 52

The probability of the union of two mutually exclusive events A and B is 0.

Question 53

NARRBEGIN: Messenger Service
Messenger Service
Three messenger services deliver to a small town in Oregon. Service A has 60% of all the scheduled deliveries, service B has 30%, and service C has the remaining 10%. Their on-time rates are 80%, 60%, and 40% respectively. Define event O as a service delivers a package on time.NARREND
{Messenger Service Narrative} If a package was delivered on time, what is the probability that it was service C?

Question 54

NARRBEGIN: Messenger Service
Messenger Service
Three messenger services deliver to a small town in Oregon. Service A has 60% of all the scheduled deliveries, service B has 30%, and service C has the remaining 10%. Their on-time rates are 80%, 60%, and 40% respectively. Define event O as a service delivers a package on time.NARREND
{Messenger Service Narrative} If a package was delivered 40 minutes late, what is the probability that it was service B?

Question 55

Julius and Gabe go to a show during their Spring break and toss a balanced coin to see who will pay for the tickets. The probability that Gabe will pay three days in a row is 0.125.

Question 56

NARRBEGIN: Messenger Service
Messenger Service
Three messenger services deliver to a small town in Oregon. Service A has 60% of all the scheduled deliveries, service B has 30%, and service C has the remaining 10%. Their on-time rates are 80%, 60%, and 40% respectively. Define event O as a service delivers a package on time.NARREND
{Messenger Service Narrative} Calculate P(A and O).

Question 57

NARRBEGIN: Messenger Service
Messenger Service
Three messenger services deliver to a small town in Oregon. Service A has 60% of all the scheduled deliveries, service B has 30%, and service C has the remaining 10%. Their on-time rates are 80%, 60%, and 40% respectively. Define event O as a service delivers a package on time.NARREND
{Messenger Service Narrative} If a package was delivered on time, what is the probability that it was service B?

Question 58

NARRBEGIN: Messenger Service
Messenger Service
Three messenger services deliver to a small town in Oregon. Service A has 60% of all the scheduled deliveries, service B has 30%, and service C has the remaining 10%. Their on-time rates are 80%, 60%, and 40% respectively. Define event O as a service delivers a package on time.NARREND
{Messenger Service Narrative} If a package was delivered 40 minutes late, what is the probability that it was service C?

Question 59

NARRBEGIN: Messenger Service
Messenger Service
Three messenger services deliver to a small town in Oregon. Service A has 60% of all the scheduled deliveries, service B has 30%, and service C has the remaining 10%. Their on-time rates are 80%, 60%, and 40% respectively. Define event O as a service delivers a package on time.NARREND
{Messenger Service Narrative} Calculate P(B and O).

Question 60

If A and B are two independent events with P(A) = 0.9 and P(B|A) = 0.5, then P(A and B) = 0.45.

Question 61

If the events A and B are independent with P(A) = 0.35 and P(B) = 0.45, then the probability that both events will occur simultaneously is:

A)0
B)0.16
C)0.80
D)Not enough information to tell.

Question 62

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)0.24
D)None of these choices.

Question 63

Two events A and B are said to be mutually exclusive if P(A and B) = 1.0.

Question 64

If A and B are independent events with P(A) = 0.60 and P(B) = 0.70, then P(A or B) equals:

A)1.30
B)0.88
C)0.42
D)Cannot tell from the given information.

Question 65

If P(A) = 0.84, P(B) = 0.76, and P(A or B) = 0.90, then P(A and B) is:

A)0.06
B)0.14
C)0.70
D)0.83

Question 66

Which of the following statements is always correct?

A)P(A and B) = P(A) * P(B)
B)P(A or B) = P(A) + P(B)
C)P(A) = 1 -P(A^c)
D)None of these choices.

Question 67

If A and B are any two events with P(A) = .8 and P(B|A) = .4, then P(A and B) is:

A).40
B).32
C)1.20
D)None of these choices.

Question 68

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

Question 69

If P(A) = 0.20, P(B) = 0.30, and P(A and B) = 0, then A and B are:

A)dependent events
B)independent events
C)mutually exclusive events
D)complementary events

Question 70

If A and B are mutually exclusive events, with P(A) = 0.20 and P(B) = 0.30, then the probability that both events will occur simultaneously is:

A)0.50
B)0.06
C)0
D)None of these choices.

Question 71

Suppose P(A) = 0.30. The probability of the complement of A is:

A)0.30
B)0.70
C)-0.30
D)None of these choices.

Question 72

Two events A and B are said to be mutually exclusive if:

A)P(A|B) = 1
B)P(A|B) = P(A)
C)P(A and B) =1
D)P(A and B) = 0

Question 73

If P(B) = .7 and P(A|B) = .7, then P(A and B) = 0.

Question 74

If A and B are mutually exclusive events with P(A) = 0.30 and P(B) = 0.40, then P(A or B) is:

A)0.10
B)0.12
C)0.70
D)None of these choices

Question 75

The ____________________ rule says that P(A^c) = 1- P(A).

Question 76

If events A and B are independent then:

A)P(A and B) = P(A) * P(B)
B)P(A and B) = P(A) + P(B)
C)P(B|A) = P(A)
D)None of these choices.

Question 77

If A and B are any two events with P(A) = .8 and P(B|A^c) = .7, then P(A^c and B) is

A)0.56
B)0.14
C)1.50
D)None of these choices.

Question 78

Events A and B are either independent or mutually exclusive.

Question 79

The ____________________ rule is used to calculate the joint probability of two events.

Question 80

If P(B) = .7 and P(B|A) = .4, then P(A and B) must be .28.