Stats Ch 4 Practice

Assume the sample space S={win,loss}. Select which fulfills the requirements of the definition of probability.

P({win})=0.8, P({loss})=0.2 (equal to 1)

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.

Permutation

The addition rule for two events A and B is **formula

P(A∪B)= P(A)+P(B)-P(A∩B)

For two events A and B, the multiplication rule is

P(A∩B)= P(A|B)xP(B)

A _________ of an experiment contains all possible outcomes of the experiment

Sample space

To calculate the union for two mutually exclusive events A and B,

we add the probability of A to the probability of B

Which of the following events are mutually exclusive? [either this will happens, or that?]

-Receiving an 'A' and receiving a 'B' as a final grade in an Accounting class. -Being on time and being late for an appointment Not: -Being of German descent and being of Mexican descent. -Passing a stats test and passing an english test.

When rolling a pair of dice and summing the two values rolled, which of the following are exhaustive events?

-a value of 6 or more and a value of 8 or less -a value of 7 or more and a value of 6 or less -an even number and an odd number. Not: a value of 9 or more and a value of 7 or less

The manufacturer of liquid laundry detergent has a 0.02 probability that the detergent bottles will be improperly filled. There is a 0.03 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

0.0006 Since the events are independent, we calculate 0.02 x 0.03 = 0.006

The High Roller Casino puts the odds of a certain baseball team winning the World Series at 1 to 30 (1:30). Based on those odds, what is the probability that this baseball team will win the WS?

0.032 (1/30?)

The intersection of events A and B, denoted A∩B, contains

all outcomes that are in A and B

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

combination

The probability of an employee getting a promotion is 0.20. The probability of an employee having an MBA is 0.30. The probability of an employee getting a promotion given that the employee has an MBA is 0.25. The probability that an employee has an MBA and gets a promotion is

0.075 P(A∩B)= P(A|B) x P(B)= 0.25 x 0.30 = 0.075

The probability of randomly selecting a "spade" from a deck of cards is

0.25 (because 4 suits in a deck)

Let P(A)=0.30 and P(B)=0.40. Suppose A and B are independent events. Calculate P(B | A)

0.40 Since A and B are independent events, P(B)=P(B|A)

The probability of Margaret receiving a promotion at XYZ corp. is 0.70. The prob of Katia receiving a promotion at ABC inc. is 0.60. If the two promotions are independent, then the probability of both Margaret and Katia receiving a promotion is _______________

0.42 Since the events are independent, 0.70 x 0.60 = 0.42

The probability of a customer purchasing popcorn at the movie theater is 0.3. What is the probability that a customer does not purchase popcorn?

0.7

The probability that Anthony is on time for work is 0.90. The probability that Anthony takes the train to work is 0.80. Given that Anthony takes the train to work, the probability that he is on time is 0.95. The probability that Anthony is on time for work and takes the train is

0.76 P(on time ∩ train) = P(on time | train) x P(train) = 0.95 x 0.80 = 0.76

In a particular industry, it is known that 82% of companies ship their products by truck and 47% of companies ship their product by rail. Forty percent of companies ship by truck and rail. The probability that a company ships by truck or rail is

0.89 0.82 + 0.47 - 0.40 = 0.89

5!=?

120 5x4x3x2x1

Mike is placing a bet on an upcoming horse race in which seven horses are running. Mike places a trifecta bet that wins only if he correctly picks the first, second, and third place horses in order. In how many different ways can Mike select three horses when order matters?

210 n!/(n-x)! = 7!/(7-3)! = 5040/24 = 210

A festival has become so popular that is 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. The odds that a random applicant does not receive a ticket are

3.76 to 1 - The odds against A occurring equal 1-P(A)/P(A)

If an experiment is selecting a card from a deck of cards, then the sample space is

All the cards in the deck (-not just face cards, red cards, aces, etc.)

The relative frequency of an event is used to calculate what type of probability?

An empirical probability

The conditional probability of A given B is calculated by diving the intersection of A and B by the probability of

B

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. (not: the probability of tossing a head on a coin is 0.5) - this is an a priori 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

For hotels in NYC, a travel web site wants to provide information comparing hotel costs (high,average,low) versus the quality ranking of the hotel (excellent, good,fair,bad). A useful way to summarize this data is to construct a

Contingency table

A trial, or process, that produces several possible outcomes is referred to as an_______

Experiment

The _______ formula is used to determine the number of possible ways to arrange (n) items when there are no groups

Factorial

True False: 0! = 0

False (0! = 1)

The probability of State College winning a football game is 0.60 The probability of University of State winning a football game is 0.65. Given that State College has won its football game, the probability that Univ of State wins its game is 0.65. The teams are not playing each other. The events State College and U of State winning are

Independent

The probability that a customer will purchase a product is 0.15. The probability that a customer is a male is 0.5. The probability that a customer is a wale and will purchase a product is 0.075. The events purchasing a product and being a male are

Independent

If A and B are independent events, then

P(A)=P(A|B)

A probability based on personal judgment rather than on observation or logical analysis is best referred to as a

Subjective probability (review correlated, empirical, and a priori, prob)

Which of the following is NOT an example of an experiment?

The winner of last weeks lottery drawing. (has only one outcome) Examples: (multiple outcomes) -asking someone who they think will win the world series -the number of computers that will be sold next month at a comp. store -selecting a card from a deck of cards

True False: When constructing a joint probability table, the cell in the lower right corner must always equal 1.0

True (the lower right cell represents all outcomes in the sample space, which is the probability 1.)

Using the multiplication rule, the probability that event A and event B both occur is computed by multiplying the conditional probability of event A given event B by the probability of

event B

Events that include all outcomes in the sample space are known as _________ events

exhaustive

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

A numerical value that measures the likelihood of an uncertain event is a ________?

Probability

A subset of the sample space is an __________

Event