Deck 4: Probability and Probability Models

Question 1

If events A and B are independent, then P(A|B) is always equal to zero.

Answer 1

False

Question 2

A subjective probability is a probability assessment that is based on experience, intuitive judgment, or expertise.

Answer 2

True

Question 3

Events that have no sample space outcomes in common, and therefore cannot occur simultaneously, are referred to as independent events.

Answer 3

False

Question 4

Bayes' Theorem is always based on two states of nature and three experimental outcomes.

Question 5

An event is a collection of sample space outcomes.

Question 6

A probability model is a mathematic representation of a random phenomenon.

Question 7

Two mutually exclusive events having positive probabilities are ________ dependent.

A) always
B) sometimes
C) never

Question 8

If events A and B are mutually exclusive, then P(A|B) is always equal to zero.

Question 9

A manager has just received the expense checks for six of her employees. She randomly distributes the checks to the six employees. What is the probability that exactly five of them will receive the correct checks (checks with the correct names)?

A) 1
B) 1/2
C) 1/6
D) 0
E) 1/3

Question 10

Mutually exclusive events have a nonempty intersection.

Question 11

In which of the following are the two events A and B always independent?

A) A and B are mutually exclusive.
B) The probability of event A is influenced by the probability of event B.
C) The intersection of A and B is zero.
D) P(A|B) = P(B|A).
E) The probability of event A is not influenced by whether event B occurs, or P(A|B) = P(A).

Question 12

There are two types of probability distributions: discrete and binomial.

Question 13

A ________ is a measure of the chance that an uncertain event will occur.

A) random experiment
B) sample space
C) probability
D) complement
E) population

Question 14

The probability of an event is the sum of the probabilities of the sample space outcomes that correspond to the event.

Question 15

In any probability situation, either an event or its complement must occur.

Question 16

Two events are independent if the probability of one event is influenced by whether or not the other event occurs.

Question 17

If events A and B are mutually exclusive, then P(A∩B) is always equal to zero.

Question 18

A random variable is a numerical value that is determined by the outcome of an experiment.

Question 19

Bayes' Theorem uses prior probabilities with additional information to compute posterior probabilities.

Question 20

The method of assigning probabilities when all outcomes are equally likely to occur is called the classical method.

Question 21

The ________ of an event is a number that measures the likelihood that an event will occur when an experiment is carried out.

A) outcome
B) probability
C) intersection
D) observation

Question 22

A(n) ________ probability is a probability assessment that is based on experience, intuitive judgment, or expertise.

A) experimental
B) relative frequency
C) objective
D) subjective

Question 23

Probabilities must be assigned to each sample space outcome so that the probabilities of all the sample space outcomes add up to ________.

A) 1
B) between 0 and 1
C) between −1 and 1
D) 0

Question 24

The set of all possible outcomes for an experiment is called a(n) ________.

A) sample space
B) event
C) experiment
D) probability

Question 25

If two events are independent, we can ________ their probabilities to determine the intersection probability.

A) divide
B) add
C) multiply
D) subtract

Question 26

A ________ is the probability that one event will occur given that we know that another event already has occurred.

A) sample space outcome
B) subjective probability
C) complement of events
D) long-run relative frequency
E) conditional probability

Question 27

If events A and B are independent, then the probability of simultaneous occurrence of event A and event B can be found with ________.

A) P(A)·P(B)
B) P(A)·P(B|A)
C) P(B)·P(A|B)
D) All of these choices are correct.

Question 28

Events that have no sample space outcomes in common, and therefore cannot occur simultaneously, are ________.

A) independent
B) mutually exclusive
C) intersections
D) unions

Question 29

Probabilities must be assigned to sample space outcomes so that the probability assigned to each sample space outcome must be between ________, inclusive.

A) 0 and 100
B) −100 and 100
C) 0 and 1
D) −1 and 1

Question 30

If events A and B are independent, then P(A|B) is equal to ________.

A) P(B)
B) P(A∩B)
C) P(A)
D) P(AUB)

Question 31

If P(A) > 0 and P(B) > 0 and events A and B are independent, then ________.

A) P(A) = P(B)
B) P(A|B) = P(A)
C) P(A∩B) = 0
D) P(A∩B) = P(A) P(B∪A)

Question 32

A probability may be interpreted as a long-run ________ frequency.

A) observational
B) relative
C) experimental
D) conditional

Question 33

When the probability of one event is influenced by whether or not another event occurs, the events are said to be ________.

A) independent
B) dependent
C) mutually exclusive
D) experimental

Question 34

A(n) ________ is a collection of sample space outcomes.

A) experiment
B) event
C) set
D) probability

Question 35

A(n) ________ is the set of all of the distinct possible outcomes of an experiment.

A) sample space
B) union
C) intersection
D) observation

Question 36

P(AUB) = P(A) + P(B) − P(A∩B) represents the formula for the ________.

A) conditional probability
B) addition rule
C) addition rule for two mutually exclusive events
D) multiplication rule

Question 37

The simultaneous occurrence of events A and B is represented by the notation ________.

A) AUB
B) A|B
C) A∩B
D) B|A

Question 38

When the probability of one event is not influenced by whether or not another event occurs, the events are said to be ________.

A) independent
B) dependent
C) mutually exclusive
D) experimental

Question 39

A process of observation that has an uncertain outcome is referred to as a(n) ________.

A) probability
B) frequency
C) conditional probability
D) experiment

Question 40

The ________ of two events X and Y is another event that consists of the sample space outcomes belonging to either event X or event Y or both events X and Y.

A) complement
B) union
C) intersection
D) conditional probability

Question 41

What is the probability of rolling a value higher than eight with a pair of fair dice?

A) 6/36
B) 18/36
C) 10/36
D) 8/36
E) 12/36

Question 42

Determine whether these two events are mutually exclusive: someone born in the United States and a U.S. citizen.

A) mutually exclusive
B) not mutually exclusive

Question 43

Consider a standard deck of 52 playing cards, a randomly selected card from the deck, and the following events: R = red, B = black, A = ace, N = nine, D = diamond, and C = club. Are R and C mutually exclusive?

A) Yes, mutually exclusive.
B) No, not mutually exclusive.

Question 44

Determine whether these two events are mutually exclusive: unmarried person and a person with an employed spouse.

A) mutually exclusive
B) not mutually exclusive

Question 45

The probability model describing an experiment consists of

A) sample space.
B) probabilities of the sample space outcomes.
C) sample space and probabilities of the sample space outcomes.
D) independent events.
E) random variables.

Question 46

Consider a standard deck of 52 playing cards, a randomly selected card from the deck, and the following events: R = red, B = black, A = ace, N = nine, D = diamond, and C = club. Are R and A mutually exclusive?

A) Yes, mutually exclusive.
B) No, not mutually exclusive.

Question 47

A lot contains 12 items, and 4 are defective. If three items are drawn at random from the lot, what is the probability they are not defective?

A) 0.3333
B) 0.2545
C) 0.5000
D) 0.2963
E) 0.0370

Question 48

Consider a standard deck of 52 playing cards, a randomly selected card from the deck, and the following events: R = red, B = black, A = ace, N = nine, D = diamond, and C = club. Are A and N mutually exclusive?

A) Yes, mutually exclusive.
B) No, not mutually exclusive.

Question 49

What is the probability of at least one tail in the toss of three fair coins?

A) 1/8
B) 4/8
C) 5/8
D) 7/8
E) 6/8

Question 50

What is the probability that a king appears in drawing a single card from a deck of 52 cards?

A) 4/13
B) 1/13
C) 1/52
D) 1/12
E) 2/13

Question 51

What is the probability of rolling a seven with a pair of fair dice?

A) 6/36
B) 3/36
C) 1/36
D) 8/36
E) 7/36

Question 52

Determine whether these two events are mutually exclusive: voter who favors gun control and an unregistered voter.

A) mutually exclusive
B) not mutually exclusive

Question 53

Determine whether these two events are mutually exclusive: consumer with an unlisted phone number and a consumer who does not drive.

A) mutually exclusive
B) not mutually exclusive

Question 54

Determine whether these two events are mutually exclusive: someone with three sisters and someone with four siblings.

A) mutually exclusive
B) not mutually exclusive

Question 55

The ________ of two events A and B is the event that consists of the sample space outcomes belonging to both event A and event B.

A) union
B) intersection
C) complement
D) mutual exclusivity

Question 56

Consider a standard deck of 52 playing cards, a randomly selected card from the deck, and the following events: R = red, B = black, A = ace, N = nine, D = diamond, and C = club. Are D and C mutually exclusive?

A) Yes, mutually exclusive.
B) No, not mutually exclusive.

Question 57

Consider a standard deck of 52 playing cards, a randomly selected card from the deck, and the following events: R = red, B = black, A = ace, N = nine, D = diamond, and C = club. Are N and C mutually exclusive?

A) Yes, mutually exclusive.
B) No, not mutually exclusive.

Question 58

What is the probability that an even number appears on the toss of a die?

A) 0.5
B) 0.33
C) 0.25
D) 0.67
E) 1.00

Question 59

The ________ of event X consists of all sample space outcomes that do not correspond to the occurrence of event X.

A) independence
B) complement
C) conditional probability
D) dependence

Question 60

If we consider the toss of four coins as an experiment, how many outcomes does the sample space consist of?

A) 8
B) 4
C) 16
D) 32
E) 2

Question 61

Container 1 has 8 items, 3 of which are defective. Container 2 has 5 items, 2 of which are defective. If one item is drawn from each container, what is the probability that both items are not defective?

A) 0.3750
B) 0.3846
C) 0.1500
D) 0.6154
E) 0.2000

Question 62

A machine is made up of 3 components: an upper part, a middle part, and a lower part. The machine is then assembled. 5 percent of the upper parts are defective, 4 percent of the middle parts are defective, and 1 percent of the lower parts are defective. What is the probability that a machine is not defective?

A) 0.1000
B) 0.9029
C) 0.8000
D) 0.0002
E) 0.7209

Question 63

A card is drawn from a standard deck. What is the probability the card is an ace, given that it is a club?

A) 1/52
B) 1/13
C) 4/13
D) 1/4

Question 64

A group has 12 men and 4 women. If 3 people are selected at random from the group, what is the probability that they are all men?

A) 0.4219
B) 0.5143
C) 0.3929
D) 0.0156
E) 0.0045

Question 65

A pair of dice is thrown. What is the probability that one of the faces is a 3, given that the sum of the two faces is 9?

A) 1/3
B) 1/36
C) 1/6
D) 1/2
E) 1/4

Question 66

A coin is tossed 6 times. What is the probability that at least one head occurs?

A) 63/64
B) 1/64
C) 1/36
D) 5/6
E) 1/2

Question 67

A card is drawn from a standard deck. Given that a face card is drawn, what is the probability it will be a king?

A) 1/3
B) 1/13
C) 4/13
D) 1/12
E) 1/4

Question 68

Container 1 has 8 items, 3 of which are defective. Container 2 has 5 items, 2 of which are defective. If one item is drawn from each container, what is the probability that the item from Container 1 is defective and the item from Container 2 is not defective?

A) 0.3846
B) 0.2250
C) 0.3750
D) 0.6154
E) 0.1500

Question 69

At a college, 70 percent of the students are women, and 50 percent of the students receive a grade of C. 25 percent of the students are neither female nor C students. Use this contingency table. If a student is male, what is the probability he is a C student?

A) 0.05
B) 0.10
C) 0.30
D) 0.17
E) 0.50

Question 70

What is the probability of winning four games in a row, if the probability of winning each game individually is 1/2?

A) 1/4
B) 1/8
C) 1/2
D) 3/16
E) 1/16

Question 71

At a college, 70 percent of the students are women, and 50 percent of the students receive a grade of C. 25 percent of the students are neither female nor C students. Use this contingency table. What is the probability that a student is female and a C student?

A) .45
B) .50
C) .70
D) .25
E) .05

Question 72

Given a standard deck of cards, what is the probability of drawing a face card, given that it is a red card?

A) 0.115
B) 0.500
C) 0.231
D) 0.462
E) 0.308

Question 73

Given the standard deck of cards, what is the probability of drawing a red card, given that it is a face card?

A) 0.500
B) 0.115
C) 0.231
D) 0.077
E) 0.308

Question 74

A machine is produced by a sequence of operations. On average, one out of every 1000 machines produced is defective. What is the probability that two machines selected at random are both nondefective?

A) 0.000999
B) 0.001
C) 0.002
D) 0.998
E) 0.500

Question 75

Container 1 has 8 items, 3 of which are defective. Container 2 has 5 items, 2 of which are defective. If one item is drawn from each container, what is the probability that only one of the items is defective?

A) 0.2250
B) 0.6250
C) 0.2500
D) 0.4750
E) 0.1500

Question 76

A family has two children. What is the probability that both are girls, given that at least one is a girl?

A) 1/8
B) 1/4
C) 1/2
D) 1/3
E) 1/6

Question 77

At a college, 70 percent of the students are women, and 50 percent of the students receive a grade of C. 25 percent of the students are neither female nor C students. Construct a contingency table.

Question 78

At a college, 70 percent of the students are women, and 50 percent of the students receive a grade of C. 25 percent of the students are neither female nor C students. Use this contingency table. What is the probability that a student is male and not a C student?

A) .45
B) .50
C) .70
D) .25
E) .05

Question 79

A person is dealt 5 cards from a deck of 52 cards. What is the probability they are all clubs?

A) 0.2500
B) 0.0962
C) 0.0769
D) 0.0010
E) 0.0005

Question 80

Independently, a coin is tossed, a card is drawn from a deck, and a die is thrown. What is the probability of observing a head on the coin, an ace on the card, and a five on the die?

A) 0.0064
B) 0.1000
C) 0.7436
D) 0.0096
E) 0.5000