IS 242 Chapter 4: Introduction to Probability
Mutually exclusive events
do not share common outcomes of the experiment.
A subset of the sample space is called a/an
event
Events are _________ if all possible outcomes of an experiment belong to the events.
exhaustive
A trial, or process, that produces several possible outcomes is referred to as a(n) ______.
experiment
An ______ is a process that leads to one of several possible outcomes.
experiment
n! denotes a _____ formula.
factorial
If two events do not influence each other, then the events are ______ events.
independent
Two events are _______ if the occurrence of one event does not affect the probability of the occurrence of the other event.
independent
It is common to refer to P(A ∩ B) as the _______ probability of events A and B.
joint
P(A ∩ B) is known as a _______ probability.
joint
The values in the interior of a contingency table represent ________ probabilities.
joint
P(A ∩ B) = P(A|B)P(B) is referred to as the _______ rule for probabilities.
multiplication
Which of these formulas is a factorial?
n!
Which of these formulas is a permutation?
n! / (n−x)!
Which of these formulas is a combination?
n!/(n−x)!x!
Since empirical and classical probabilities generally do not vary from person to person, they are often grouped as ________ probabilities.
objective
The sum of the probabilities of a list of mutually exclusive and exhaustive events is...
one
A numerical value that measures the likelihood of an uncertain event is a ______.
probability
A probability based on personal judgment rather than on observation or logical analysis is best referred to as a(n)
subjective probability.
A softball coach believes that Laurie has a 0.5 probability of getting a hit against a particular pitcher that Laurie has never batted against before. This type of probability is BEST characterized as a(n):
subjective probability.
The _______ probability rule is a useful tool for breaking the computation of a probability into distinct cases.
total
In order to convert a contingency table into a joint probability table, the frequency of each cell is divided by the
total number of outcomes in the sample space.
The values in the margins of a contingency table represent ________ probabilities.
unconditional
To calculate the probability of the union of two mutually exclusive events A and B,
we add the probability of A to the probability of B.
For mutually exclusive events A and B, the joint probability is
zero
Probability values range from...
zero to one.
How many outcomes of an experiment constitute a simple event?
One
If A and B are independent events, then
P(A)=P(A|B)
The complement rule with respect to event A is...
P(AC) = 1 - P(A)
The addition rule for two events A and B is...
P(AuB) = P(A) + P(B) - P(AnB)
For two events A and B, the multiplication rule is...
P(A∩B) = P(A|B) × P(B).
Assume the sample space S = {win, loss}. Which numbers define valid probabilities?
P({win}) = 0.8, P({loss}) = 0.2
Which of the following events are mutually exclusive?
Receiving an 'A' and receiving a 'B+' as a final grade in an Accounting class. Being on time and being late for an appointment.
A sample space, denoted by
S
Which of the following is an example of a conditional probability?
The probability that Lisa purchases groceries, given that Neil has already purchased groceries.
Bayes' theorem is calculated by using what rule in the denominator?
The total probability rule.
Which method can be used to help implement the total probability rule?
A probability table
The relative frequency of an event is used to calculate what type of probability?
An empirical probability
Which of the following BEST represents an empirical probability?
Based on past data, a manager believes there is a 70% chance of retaining an employee for at least one year.
_______ theorem uses total probability rule to update the probability of an event that has been affected by a new piece of evidence.
Bayes'
When updating a prior probability based on new information, which of the following methodologies is MOST useful?
Bayes' Theorem
This probability is based on logical analysis rather than on observation or personal judgment.
Classical
______ probabilities are based on the assumption that all outcomes of an experiment are equally likely.
Classical
Which of the following is NOT an example of an experiment?
Determine a historical fact such as the name of the U.S. President in the year 1856.
When constructing a joint probability table, the cell in the lower right corner must always equal 1.0.
True
The complement of event A within the sample space S contains
all outcomes in S that are not in A.
The intersection of events A and B, denoted A∩B, contains:
all outcomes that are in A and B.
If an experiment is selecting a card from a deck of cards, then the sample space is
all the cards in the deck.
A probability based on logical analysis rather than on observation or personal judgment is BEST referred to as a(n):
classical probability.
For any given event, the probability of that event and the probability of the ______ of the event must sum to one.
complement
A ______ probability is the probability of an event given that another event has already occurred.
conditional
The total probability rule is used to compute an unconditional probability of an event by using...
conditional probabilities.
A ______ _______ shows the frequencies for two categorical variables, x and y, where each cell represents a mutually exclusive combination of the pair of x and y observations.
contingency table
For hotels in New York City, a travel web site wants to provide information comparing hotel costs (high, average, low) versus the quality ranking of the hotel (excellent, good, fair, poor). A useful way to summarize these data is to construct a(n)
contingency table.
