Deck 4: A: probability and Probability Distributions

Question 1

Which of the following may be used to represent the sample space of an experiment?

A) a joint probability table
B) the additive rule of probability
C) the multiplicative rule of probability
D) a tree diagram

Answer 1

D

Question 2

What is any subset of the sample space called?

A) an event
B) an experiment
C) a mutually exclusive event
D) independent events

Answer 2

A

Question 3

Which of the following is a useful graphical method for displaying the sample space of an experiment?

A) a tree diagram
B) a box plot
C) a histogram
D) a scatterplot

Answer 3

A

Question 4

Suppose P(A) = 0.4, P(B) = 0.3, and P(A B) = 0. Which one of the following statements correctly defines the relationship between events A and B?

A) Events A and B are independent, but not mutually exclusive.
B) Events A and B are mutually exclusive, but not independent.
C) Events A and B are neither mutually exclusive nor independent.
D) Events A and B are both mutually exclusive and independent.

Question 5

What is the set of all simple events of an experiment called?

A) a compound event
B) a sample space
C) a population
D) a random sample

Question 6

If P(A/B) = P(A), or P(B/A) = P(B), which of the following best describes the events A and B?

A) They are mutually exclusive.
B) They are disjoint.
C) They are independent.
D) They are dependent.

Question 7

If P(A) = 0.42 and P(B) = 0.38, then what is P(A B)?

A) 0.80
B) 0.58
C) 0.04
D) cannot be determined from the information given

Question 8

When Cynthia enters a grocery store, there are three simple events: buy nothing, buy a small amount, or buy a large amount. In this situation, if Cynthia buys a small amount, she cannot also buy a large amount or buy nothing. How may one best classify these three events?

A) They are mutually exclusive events.
B) They are not mutually exclusive events.
C) They are dependent events.
D) They are independent events.

Question 9

If P(A) = 0.40, P(B) = 0.30, and P(A B) = 0.12, then what could you deduce about the events A and B?

A) They are dependent events.
B) They are independent events.
C) They are mutually exclusive events.
D) They are disjoint events.

Question 10

Which of the following best describes all the outcomes (simple events) contained in one or the other of two random events, or possibly in both?

A) the events of an experiment
B) the intersection of two events
C) the probability space of an experiment
D) the union of two events

Question 11

If P(A) = 0.30, P(B) = 0.40, and P(A B) = 0.20, what is the value of P(A/B)?

A) 0.08
B) 0.12
C) 0.50
D) 0.67

Question 12

If events A and B are mutually exclusive, then what is the probability of both events occurring simultaneously?

A) -1
B) 0
C) 1
D) any value between 0 and 1

Question 13

Suppose that an experiment consists of tossing three unbiased coins simultaneously. How many simple events are contained in this experiment?

A) 3
B) 6
C) 8
D) 9

Question 14

What does the notation represent?

A) the union of two events
B) the intersection of two events
C) the complement of an event
D) the additive rule of probability

Question 15

Suppose you are told that an experiment consists of three stages and that there are three ways to accomplish the first stage, four ways to accomplish the second stage, and five to accomplish the third stage. What would be the number of ways to accomplish the experiment?

A) 12
B) 15
C) 20
D) 60

Question 16

Which of the following is the best description of an event?

A) an experiment that is not controlled by the decision maker
B) the list of all possible simple events of an experiment
C) a collection of one or more simple events
D) a collection of two or more simple events

Question 17

How many ways can one choose a combination of three items out of eight distinct items?

A) 28
B) 56
C) 112
D) 224

Question 18

If P(A) = 0.80, P(B) = 0.70, and P(A B) = 0.90, then what is the value of P(A B)?

A) 0.56
B) 0.60
C) 0.63
D) 0.72

Question 19

Which of the following correctly describes experiments?

A) They are two random events, A and B, such that the probability of one event is not affected by the occurrence of the other event; therefore, P(A) = P(A|B).
B) They are different events that have no outcomes in common.
C) They are activities that result in one and only one of several clearly defined possible outcomes and from which one may not predict, in advance, which of these outcomes will prevail in any particular instance.
D) They are different events that have different outcomes.

Question 20

What is the sum of the probability of an event and the probability of its complement?

A) -1
B) 0
C) 1
D) any value between 0 and 1

Question 21

Which of the following is a (are) required condition(s) for the distribution of a discrete random variable that can assume values ?

A)
B)
C) Both (a) and (b) are required conditions.
D) The population data of the distribution must be quantitative.

Question 22

The probability of an event A is equal to the sum of the probabilities of the simple events contained in A.

Question 23

Relative frequency histograms are constructed for a sample of n measurements drawn from the population, whereas the probability histogram is constructed as a model for the entire population of measurements.

Question 24

Which of the following correctly describes the nature of discrete quantitative variables?

A) They can assume values only at specific points on a scale of values, with inevitable gaps between successive observations.
B) When dealing with such variables, we can count all possible observations and, with some exceptions, that count leads to a finite result.
C) Discrete quantitative variables are correctly described by both (a) and (b).

Question 25

The probability distribution of the number of accidents in North York, Ontario, each day is given by Which of the following could be used to describe this distribution?

A) a continuous probability distribution
B) a discrete probability distribution
C) a conditional probability distribution
D) an expected value distribution

Question 26

In the case of independent events A, B, and C, which of the following is equal to ?

A) P(A|B)P(B|C)P(C|A)
B) P(A|B) + P(B|C) + P(C|A)
C) P(A)P(B)P(C)
D) P(A) + P(B) + P(C)

Question 27

Which of these statements is a property of the probability distribution for a discrete random variable x ?

A) The probabilities must be nonnegative.
B) The probabilities must sum to 1.
C) The random variable must take on positive values between 0 and 1.
D) Both (a) and (b) are true.

Question 28

Probability is the tool that allows the statistician to use sample information to make inferences about or describe the population from which the sample was drawn.

Question 29

A false negative in screening tests (e.g., steroid testing of athletes) represents which of the following events?

A) The test is negative for a given condition, given that the person does not have the condition.
B) The test is positive for a given condition, given that the person does not have the condition.
C) The test is negative for a given condition, given that the person has the condition.
D) The test is positive for a given condition, given that the person has the condition.

Question 30

Which of the following clearly describes the general multiplicative rule of probability?

A) It is a rule of probability theory that is used to compute the probability for the occurrence of a union of two or more events: for any two events, A and B,
B) It is a rule of probability theory that is used to compute the probability for the occurrence of a union of two or more events: for any two events A and B,
C) It is a rule of probability theory that is used to compute the probability for an intersection of two or more events: for any two events, A and B,and also = P(B)P(A|B)
D) It is a rule of probability theory that is used to compute the probability for an intersection of two or more events: for any two events A and B,

Question 31

A false positive in screening (e.g., home pregnancy tests) may be best described by which of the following events?

A) The test is negative for a given condition, given that the person does not have the condition.
B) The test is positive for a given condition, given that the person does not have the condition.
C) The test is negative for a given condition, given that the person has the condition.
D) The test is positive for a given condition, given that the person has the condition.

Question 32

What would be the expected number of heads turning up in 500 tosses of an unbiased coin?

A) 150
B) 200
C) 250
D) 300

Question 33

Screening tests (e.g., HIV testing) are evaluated on the probability of a false negative or a false positive. How may one classify these probabilities?

A) They are both conditional probabilities.
B) They measure the probability of the intersection of two events.
C) They measure the probability of the union of two events
D) They are both marginal probabilities.

Question 34

Two events, A and B, are said to be dependent if and only if what condition is true?

A) P(A) = P(B).
B) P(A) increases along with P(B).
C) P(A) increases as P(B) decreases.
D) Event A is affected or changed by the occurrence of event B.

Question 35

The probability distribution of the number of accidents in North York, Ontario, each day is given in the table below: Based on this distribution, what is the approximate value of the standard deviation of the number of accidents per day?

A) 6.95
B) 2.64
C) 2.33
D) 1.53

Question 36

What may NOT be said about the mean of a discrete random variable x?

A) It is denoted by.
B) It is the middle value of its probability distribution.
C) It is denoted by E(x), because it is the value of x one can expect to find, on average, by numerous repetitions of the random experiment that generates the variable's actual values.
D) It is correctly described by both (a) and (b).

Question 37

The probability distribution of the number of accidents in North York, Ontario, each day is given by Based on this distribution, what would be the expected number of accidents on a given day?

A) 4.62
B) 2.15
C) 1.81
D) 1.47

Question 38

Statistics provides ways to reason from the population to the sample, whereas probability acts in reverse, moving from the sample to the population.

Question 39

What is the term for a table, formula, or graph showing all possible values that a random variable x can assume, together with their associated probabilities p(x)?

A) a discrete probability distribution
B) a continuous probability distribution
C) a bivariate probability distribution
D) the law of total probability

Question 40

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, given the fact that another event has already occurred or is certain to occur.
C) It is a measure of the likelihood of the simultaneous occurrence of two or more events.
D) It is a direct way for defining the sample space of an experiment.
It is measure of the likelihood that either one or the other out of a possible two events will occur.

Question 41

The probability of getting two heads when tossing a fair coin twice is 1/4.

Question 42

The experiment of drawing a single card once from a standard deck contains four events.

Question 43

An event is a collection of one or more simple events of an experiment.

Question 44

The probability of getting a 15 when randomly drawing a card from a well-shuffled deck is 4/52.

Question 45

Suppose that an experiment consists of tossing four unbiased coins simultaneously. The number of simple events in this experiment is 16.

Question 46

The experiment of tossing a single coin once contains one simple event.

Question 47

A tree diagram is a listing of all the simple events of an experiment.

Question 48

If an investor were interested in assessing the probability that a new supermarket will be successful in a Calgary market area, he would most likely use the relative frequency definition of probability as the method for assessing the probability of success.

Question 49

An experiment is any activity that results in one and only one of several clearly defined possible outcomes, but does not allow us to tell in advance which of these will prevail in any particular instance.

Question 50

The probability of getting the king of diamonds when randomly drawing a card from a well-shuffled deck is 1/52.

Question 51

Suppose that a patient who is complaining of several specific symptoms arrives at a doctor's office and the doctor says that she is 90% certain that the patient has the flu. In this case, it is likely that she is basing her assessment on the relative frequency approach of assigning probabilities.

Question 52

Combinations are distinguishable ordered arrangements of items, all of which have been drawn from a given group of items.

Question 53

In general, the simple events of an experiment take on values between 0 and 1.0, inclusive.

Question 54

Different events that have no outcomes in common are mutually exclusive events.

Question 55

The experiment of rolling a single die once contains six simple events.

Question 56

The sum of the probabilities for all simple events in the sample space equals 1.

Question 57

The probability of getting a black card when randomly drawing a card from a well-shuffled deck is 1/2.

Question 58

The experiment of spinning the Monte Carlo roulette wheel once contains 27 simple events.

Question 59

Invariably, Venn diagrams illustrate the intersection of two events.

Question 60

An experiment is the process by which an observation or measurement is obtained.

Question 61

The intersection of events A and B is the event that A or B or both occur.

Question 62

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

Question 63

If P(A) = 0, P(B) = 0.4, and P(A B) = 0, then events A and B are independent.

Question 64

If P(A) = 0.3, P(A B) = 0.7, and P(A B) = 0.2, then P(B) = 0.2.

Question 65

The complement of an event A, denoted by , consists of all the simple events in the sample space S that are not in A.

Question 66

The conditional probability of event B, given that event A has occurred is defined by .

Question 67

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

Question 68

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

Question 69

If P(A) = 0.4, P(B) = 0.5, and P(A B) = 0.7, then P(A B) = 0.2.

Question 70

The probability that event A will not occur is 1 - .

Question 71

If P(A) = 0.60, P(B) = 0.40, and P(B/A) = 0.60, then P(A/B) = 0.24.

Question 72

If P(A) > 0 and P(B) > 0, then when A and B are mutually exclusive events, they are also dependent events.

Question 73

Suppose A and B are mutually exclusive events where P(A) = 0.2 and P(B) = 0.3, then P(A B) = 0.5.

Question 74

If P(A/B) = P(A), then events A and B are said to be independent.

Question 75

Two events A and B are said to be mutually exclusive if P(A B) = 0.

Question 76

Conditional probability is the probability that an event will occur, with no other events taken into consideration.

Question 77

If P(A) = 0.4, P(B) = 0.5, and P(A B) = 0.20, then the events A and B are mutually exclusive.

Question 78

Suppose A and B are mutually exclusive events where P(A) = 0.1 and P(B) = 0.7, then P(A B) = 0.8.

Question 79

If A and B are two independent events with P(A) = 0.25 and P(B) = 0.45, then P(A B) = 0.70.

Question 80

If A and B are independent events with P(A) = 0.30 and P(B) = 0.50, then P(A/B) is 0.15.