Business Stats Chapter 5 Probibility
The probability of Murali going to the coffee shop is 0.7. The probability of Connie going to the coffee shop is 0.4. If Murali goes to the coffee shop, the probability of Connie going to the coffee shop is 0.48. The events Murali going to the coffee shop and Connie going to the coffee shop are
dependent
Assume P(A) = .3 and P(B) = .4. If the P(A or B) = .7 we can say that A and B are
disjoint mutually exclusive
Probabilities that are estimated from observed frequencies are called
empirical.
A contingency table is sometimes called an r x c table where r stands for number of ________ and c stands for number of_______
Blank 1: rows or row Blank 2: columns or column
A probability assigned by a person that is based on that person's judgment or experiences is a _______ probability.
Blank 1: subjective
A probability assigned by a person that is based on that person's judgment or experiences is a ________ probability
Blank 1: subjective
A _____ diagram can help a business planner visualize all possibles outcomes of a decision.
Blank 1: tree
A prior probability for event A is the _________ probability whereas the posterior probability of event A is the _______ probability
Blank 1: unconditional or marginal Blank 2: conditional
A probability that can be deduced through logical reasoning before an experiment is performed is what type of probability?
Classical
Probabilities that are estimated from observed frequencies are called
Empirical
Consider rolling two dice. Which of the following describe two events that are collectively exhaustive? Event 1: A value of 6 or more. Event 2: A value of 8 or less. Event 1: A value of 7 or more. Event 2: A value of 6 or less. Event 1: Rolling an even number. Event 2: Rolling an odd number. Event 1: A value of 9 or more. Event 2: A value of 7 or less.
Event 1: A value of 6 or more. Event 2: A value of 8 or less. Event 1: A value of 7 or more. Event 2: A value of 6 or less. Event 1: Rolling an even number. Event 2: Rolling an odd number.
Consider rolling two dice. Which of the following describe two events that are collectively exhaustive?
Event 1: A value of 7 or more. Event 2: A value of 6 or less. Event 1: Rolling an even number. Event 2: Rolling an odd number. Event 1: A value of 6 or more. Event 2: A value of 8 or less.
True or false: The General Law of Multiplication is used to calculate the probability of the union of two events.
False
True or false: The probability of winning a lottery is .0000000012. The Law of Large Numbers says that because this probability is so small, no one should ever win a lottery.
False
True or false: Tree diagrams are rarely used in business planning.
False
True or false: 0! = 0
False Reason: 0! is defined as 1, not 0.
Which of the following are examples of conditional probabilities?
If Neil has already purchased groceries, then the probability of Colleen purchasing groceries. The probability of Angel going to the movie, given that Derrick is going to the movie.
The multiplication rule is used to calculate what type of probability?
Joint
Which of the following is not an example of an experiment?
Pick the team that won last year's World Series.
If an event is getting a letter grade of A in your statistics class, what is the complement of receiving an A?
Receiving any grade except an A.
A softball coach believes that Laurie has a .3 probability of getting a hit against a left-handed pitcher that Laurie has never batted against before. The .3 probability that the coach has assigned is what type of probability?
Subjective
True or false: Probability is a number that describes uncertainty.
True
A travel web site wants to provide information comparing hotel costs versus the quality ranking of the hotel for hotels in New York City. One way to summarize this data would be
a contingency table.
Binary events are those that
are collectively exhaustive are mutually exclusive
The ______ approach to assigning probability is often used before we actually observe an experiment and often assumes each outcome is equally likely.
classical
Events that include more than one outcome from the sample space are known as _______ events.
compound
A tree diagram has ________ probabilities at the terminal end of each branch.
conditional
Using the multiplication rule, the joint probability of event A and event B is computed by multiplying the conditional probability of event A given event B by the probability of
event B.
A subset of the sample space is a/an
event or events
Events that cannot both occur at the same time are mutually ______ events.
exclusive
The _____ rule is useful for counting the possible arrangements of any n items..
factorial
The people who are involved in which of the following areas talk more commonly about odds rather than speaking of probability:
games of chance sports
If two events do not affect each of their individual probabilities then the events are ______ events.
independent
The probability of State College winning a football game is .6. The probability of University of State winning a football game is .65. Given that State College has won its football game, the probability of University of State winning its game is .65. The teams are not playing each other. The events State College winning and University of State winning are
independent.
If two events are independent, then the joint probability of the two events is calculated by
multiplying the probability of the two events.
Define event A = {1, 2, 3, 4} and event B = {6, 7, 8}. A ∩ B =
null set
Contingency tables are useful to analyze
relative frequencies The results of a survey.
The addition rule is used to calculate
the union of two events.
To calculate a joint probability from a contingency table, the frequency of each cell is divided by the
total number of outcomes in the sample space.
The _______ of two events, A and B, contains all the outcomes in either A or B or both A and B.
union
Probability values range from ______ to ______.
zero; one
Define event A = {1, 2, 3, 4} and event B = {2, 3, 6, 7}. A ∪ B =
{1, 2, 3, 4, 6, 7}
Define event A = {1, 2, 3, 4} and event B = {2, 3, 6, 7}. A ∩ B =
{2, 3,}
The _____ formula is used to determine the number of ways to arrange x objects from a group of n objects where the order of the objects matters.
Blank 1: permutation or permutations
An important theorem in probability states that as the number of trials increase, an empirical probability will approach the theoretical probability. This theorem is called the
Blank 1: law Blank 2: large Blank 3: numbers
A coach observes Tom making 10 free throws out of his last 30 attempts. Using the empirical approach, the coach assigns a probability of _________ to Tom making his next free throw. (Round probability to one decimal place.)
.3 or 0.3
Given P(A) = .4, P(B) = .6, and P(A and B) = .2, calculate the conditional probability of A given B.
.3333
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 _______ (state your answer as a decimal and round your answer to two decimal places).
.88 or 0.88
82% of companies ship their products by truck. 47% of companies ship their product by rail. 40% of companies ship by truck and rail. What is the probability that a company ships by truck or rail?
.89
The sportsbook at the High Roller Casino put the odds of a certain baseball team to win the World Series at 1:25 (1 to 25). Based on those odds, what is the probability that this baseball team will win the World Series?
0.0385
The probability of an employee getting a promotion is 0.2. The probability of an employee having an MBA is 0.3. The probability of an employee getting a promotion given that the employee has an MBA is 0.28. What is the probability that an employee has an MBA and gets a promotion?
0.084
The probability of randomly selecting a "spade" from a deck of cards is
0.25
The probability of a customer purchasing popcorn at the movie theater is 0.3. What is the probability that a customer will not purchase popcorn?
0.7
82% of companies ship their products by truck. 47% of companies ship their product by rail. 40% of companies ship by truck and rail. What is the probability that a company ships by truck or rail?
0.89
The sum of the probabilities of all the outcomes in the sample space is
1 (one).
Define event A = {1, 2, 3, 4} and event B = {2, 3, 6, 7}. A ∩ B =
2,3
A restaurant manager has 10 wait staff on duty but business has slowed down for the night and she needs to let 4 of the staff go home. How many different ways could she choose which 4 get to leave early?
210
A trial, or process, that produces several possible outcomes that cannot be known in advance is called an/a
Blank 1: random Blank 2: experiment
A festival has become so popular that it must limit the number of tickets it issues. People who hope to attend the festival send in a request for tickets, and requests are filled by random selection. Only 21% of the ticket requests are fulfilled. What are the odds of not receiving a ticket for a random applicant?
3.76 to 1
Students who take the College Prep English Course the summer before entering college have a .84 probability of achieving a "B" or better in their freshman English class at college. The odds a student taking the Prep Course will receive a "B" or better in the freshman English class are
5.25 to 1
G. Amitri is the coach of the high school mathletes team. There are 8 mathletes, but only 5 may represent the school at the upcoming math tournament. How many ways can G. Amitri randomly choose 5 mathletes from the 8 eligible mathletes?
56 Reason: n!(n−x)!(x!)n!n-x!x!=8!(8−5)!(5!)8!8-5!5!=40,328(6)(120)40,3286120=56 (n!)/(n-x)!(x!) = 8!/(8-5)!(5!) = 40,328/(6)(120) = 56
Graduates with the top three highest GPAs will be honored at the school's graduation ceremony. The highest GPA will receive the Gold Award, the second highest will received the Silver Award, and the third highest GPA will receive the Bronze Award. If there are 10 graduating seniors, how many different arrangements of honored students are possible?
720 Reason: 10!/(10-3)!
Which theorem provides a method for revising probabilities to reflect new information?
Bayes' Theorem
Which of the following events are mutually exclusive?
Being on time and being late for an appointment. Rolling an odd number and an even number on the same roll of a die.
A manufacturer of liquid laundry detergent has a .02 probability that the detergent bottles will be improperly filled. (Either too much or too little detergent.) There is a .03 probability that the label on the bottle will not be affixed properly. If the events of bottle fill and affixing the label are independent, then the probability of a bottle being filled improperly and having an improperly affixed label is ______ (round your answer to four decimal places).
Blank 1: .0006 or 0.0006
XYZ Corp. has filled 100,000 purchase orders during its existence. 1,100 of the purchase orders have had errors. Using an empirical probability, the probability of the next purchase order having an error is _______ (round your answer to three decimal places and enter as a probability not a percentage).
Blank 1: .011 or 0.011
The probability of Margaret getting a promotion at XYZ Corp. is 0.7. The probability of Katia getting a promotion at ABC Inc. is 0.6. If the two promotions are unrelated, then the probability of both Margaret and Katia receiving a promotion is ________ (round to 2 decimal places).
Blank 1: .42 or 0.42
If the events A and B are independent and P(A) = .4 and P(A and B) = .2 then P(B) =
Blank 1: .5, 0.5, or 1/2
The probability of Anthony being on time for work is 0.9. The probability that Anthony will take the train to work is 0.8. The probability that Anthony will be on time for work if he took the train is 0.95. The probability that Anthony is on time for work and took the train is _______ (2 decimal places).
Blank 1: .76 or 0.76
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 _______ (state your answer as a decimal and round your answer to two decimal places).
Blank 1: .88 or 0.88
The event A cannot occur if the P(A) =
Blank 1: 0 or zero
In order to make sure Sam gets to his final exam on time he sets 3 alarm clocks that work independently of each other. Assume the probability of any one of the alarms working is equal to .98. What is the probability that Sam is late to his final exam?
Blank 1: 0.000008 or .000008
The probability of Anthony being on time for work is 0.9. The probability that Anthony will take the train to work is 0.8. The probability that Anthony will be on time for work if he took the train is 0.95. The probability that Anthony is on time for work and took the train is ____________(2 decimal places).
Blank 1: 0.125 or .125
The odds against a horse winning a race were set at 7 to 1. The probability of that horse not winning the race is _________
Blank 1: 0.875 or .875
Mike is placing a bet on an upcoming horse race in which 7 horses are running. Mike places a trifecta bet that wins only if he correctly picks the first, second, and third place horses in order. There are ____________ possible outcomes for the first 3 horses in the correct order.
Blank 1: 210
_________ data is collected through observation.
Blank 1: Empirical
Events are considered _______ ___________ if the union of these events is the entire sample space.
Blank 1: collectively Blank 2: exhaustive
The _______ formula is used to determine the number of different ways to arrange a group of x objects from a total of n objects and the order of the objects is irrelevant.
Blank 1: combination or combinations
A ________ probability is the probability of an event given that another event has already occurred.
Blank 1: conditional
A __________ probability is the probability of an event given that another event has already occurred.
Blank 1: conditional
A tree diagram has ______ probabilities at the terminal end of each branch.
Blank 1: conditional
The three ways of assigning probability are _________ , ________ , and ________.
Blank 1: empirical Blank 2: classical Blank 3: subjective
Events that cannot both occur at the same time are mutually ______ events
Blank 1: exclusive
The ________ (one word) of two events A and B contains only those outcomes that are in both A and B.
Blank 1: intersection
