Chapter 4 assign.
How would you express the probability that a customer at the movie theater will order a drink (D) given that the customer orders popcorn (P)?
P(D|P)
A numerical value that measures the likelihood of an uncertain event is a ______.
probability
The addition rule for two events A and B is
P(A) + P(B) - P(A∩B)
If A and B are independent events, then
P(A) = P(A|B) Reason: In words: The chances for A don't change if B occurs.
The complement rule with respect to event A is Multiple choice question.
P(AC) = 1 - P(A)
For two events A and B, the multiplication rule is
P(A∩B) = P(A|B) × P(B). Reason: The multiplication rule finds the intersection, not the union.
Let event Z be an outcome of an experiment. What are possible probabilities for Z? Select all that apply.
0 1.00 0.12
When rolling a pair of dice and summing the two values rolled, which of the following are exhaustive events? Select all that apply.
A sum of 6 or more and a sum of 8 or less. A sum of 7 or more and a sum of 6 or less. An even number and an odd number.
Suppose you have flipped a fair coin 10 times and all 10 flips have come up tails. What does the law of large numbers indicate will happen?
After many more flips, the empirical results will approach 50% heads and 50% tails.
What assumption is made with classical method of determining probabilities?
All outcomes are equally likely.
Which of the following BEST represents an empirical probability?
Based on past data, a manager believes there is a 83% selling out of a particular product today. Reason: Empirical probabilities are calculated from observed data.
When updating a prior probability based on new information, which of the following methodologies is MOST useful?
Bayes' Theorem
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. Reason: There is only one possible outcome (president) in the year 1856.
A statistics student interviews for a job. After being asked what her chances of getting the job are, she states that the thinks she has an 80% chance of getting the job. What type of method did she use to determine this probability?
Subjective Empirical Reason: She can't repeat this experiment of interviewing over and over. Classical Reason: Classical would say there are two outcomes (gets job, doesn't get job) and each are equally likely.
Which method(s) can be used to help implement the total probability rule? Select all that apply.
Tabular method. A probability tree
Which of the following is an example of a conditional probability?
The probability that Lisa passes the test, given that she attends class and does the homework.
The conditional probability of A given B is calculated by dividing the probability of intersection of A and B by the probability of
b. Reason: The denominator is always the probability of the given event.
A probability based on logical analysis rather than on observation or personal judgment is BEST referred to as a(n):
classical probability.
The fact that an empirical probability will approach the classical probability if an experiment is conducted many times is known as the
law of large numbers.
Probability values range from
0 to 1
Kareem is trying to decide which college to attend full time next year. Kareem believes there is a 55% chance that he will attend State College and a 33% chance that he will attend Northern University. The probability that Kareem will attend either State or Northern is ______ .
0.88 Reason: 0.55 + 0.33 = 0.88 (mutually exclusive events)
Quantitative variables can be summarized in a contingency table by doing which of the following?
Create categories for the quantitative variables.
Assume the sample space S = {win, lose}. Which numbers define valid probabilities?
P(win) = 0.8, P(lose) = 0.2
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 is the probability of an event given that another event has already occurred.
conditional
Mutually exclusive and exhaustive events
contain all outcomes in an experiment and do not share common outcomes.
A subset of the sample space is called a/an ______.
event
Using the multiplication rule, the probability that event A and event B both occur is computed by multiplying the conditional probability of event Agiven event B by the probability of
event B.
A trial, or process, that produces several possible outcomes is referred to as a(n) ______.
experiment
The values shown in interior of a joint probability table (not the last rows or columns) are called
joint probabilities.
The total probability rule is used to compute the probability of an event by using
joint probabilities. conditional probabilities.
The sum of the probabilities of a list of mutually exclusive and collectively exhaustive events is
one.
A softball coach believes that Laurie has a 0.25 probability of getting a hit against a particular pitcher that Laurie has never batted against before. What method was used to assign this probability?
subjective probability.
The probability that Lisa passes the test, given that she attends class and does the homework.
the product of the individual probabilities.
The addition rule is used to calculate
the union of two events.
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.
Contingency tables are useful to analyze
two categorical variables.
For any given event, the probability of that event and the probability of the complement of the event must sum to ___.
1.0
When constructing a joint probability table, the cell in the lower right corner must always equal
1.0
When considering the union of two events, A and B, which ones of the following would be included? Select all that apply.
The outcomes that are in both events A and B. The outcomes that form event A. The outcomes that form event B.
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) Multiple choice question.
contingency table.
The relative frequency of an event is used to calculate what type of probability?
An empirical probability
If two events do not influence each other, then the events are ______ events.
independent
The values shown in the last row (Total) or last column (Total) of a joint probability table are called
marginal probabilities.
A(n) ______ of an experiment contains all possible outcomes of the experiment.
sample space
Why does the addition rule for mutually exclusive events not subtract the intersection of the two events?
Because their intersection is 0.
How many outcomes of an experiment constitute a simple event?
One
Which one of the following words is associated with the union of two events?
Or
Sometimes the union of two events will be overstated if the union is found by adding just the individual probabilities. What is done to keep from overstating the probability of the union of two events?
The intersection of the event is subtracted.
Bayes' theorem is calculated by using what rule in the denominator?
The total probability rule.
Based on past data, the probability that a new hire at Company XYZ will be successful is 0.70. The company has started using an applicant screening test. Given the applicant scores well on the test, the probability the new hire will be successful is 0.70. The events 'new hire being successful' and 'applicant scoring well' are
independent.
The probability that a customer will purchase a product is 0.20. The probability that a customer is a male is 0.5. The probability that a customer is a male and will purchase a product is 0.10. The events of purchasing a product and being a male are
independent. Reason: Independent since P(A) × P(B) = 0.2 × 0.5 = 0.1 = P(A ∩ B)
If two events are independent, then the probability that both events occur equals
the product of the individual probabilities.
