Quantitative Survey Methods Ch4

A conditional probability is computed as follows :

P(A|B) = 𝑃 (𝐴 ∩ 𝐵) / 𝑃 (𝐵)

the multiplication law is written as:

P(A∩B) = P(B)P(A|B)

The addition law for mutually exclusive events is:

P(A∪B) = P(A) + P(B)

The _______________ law provides a way to compute the probability of the intersection of two events.

multiplication

Two events are ____________ __________ if, when one event occurs, the other cannot occur.

mutually exclusive

A decision maker subjectively assigned the following probabilities to the four outcomes of an experiment: P(E1)=.10, P(E2)=.15, P(E3)=.40, and P(E4)=.20 Are these probability assignments valid? Explain.

no, they are greater than or equal to 0, but do not sum to 1

A probability near _____ indicates an event is almost certain to occur.

one

The different probability estimates emphasize the __________ nature of the subjective method.

personal

The probability of any event is equal to the sum of the ______________ of the sample points in the event.

probabilities

In statistical experiments, _______________ determines outcomes.

probability

In statistical experiments, ________________ determines outcomes.

probability

Even though the experiment is repeated in exactly the same way, an entirely different outcome may occur. For this reason, statistical experiments are sometimes called ___________ experiments.

random

An experimental outcome is also called a ___________ _______.

sample point

Two events are said to be mutually exclusive if the events have no ___________ ________ in common.

sample points

The ___________ _________ for an experiment is the set of all experimental outcomes.

sample space

The best probability estimates often are obtained by combining the estimates from the classical or relative frequency approach with the ________________ estimate.

subjective

A helpful graphical representation of a multiple-step experiment is a ________ diagram.

tree

t or f: If we can identify all the sample points of an experiment and assign a probability to each, we can compute the probability of an event.

true

Managers often base their decisions on an analysis of ______________ such as the following: What are the chancesthat sales will decrease if we increase prices? What is the likelihooda new assembly method will increase productivity? What are the oddsthat a new investment will be profitable?

uncertainties

The _________ of events A and B is the event containing all sample points that are in A or B or both.

union

The __________ of events A and B is denoted by A∪B.

union

A probability near zero indicates an event is quite __________ to occur.

unlikely

basic probability relationships that can be used to compute the probability of an event without knowledge of all the sample point probabilities:

- Complement of an Event - Union of Two Events - Intersection of Two Events - Mutually Exclusive Events

If events A and B are mutually exclusive, P(A∩B) = ___.

0

Probability values are always assigned on a scale from ___ to ___.

0 to 1

Basic Requirements for Assigning Probabilities: 2. The sum of the probabilities for all experimental outcomes must equal _____. P(E1) + P(E2) + . . . + P(En) = 1 where: nis the number of experimental outcomes

1

How many permutations of three items can be selected from a group of six? Use the letters A,B,C,D,E, and F to identify the items.

120

An experiment has three steps with three outcomes possible for the first step, two outcomes possible for the second step, and four outcomes possible for the third step. How many experimental outcomes exist for the entire experiment?

24

_________ ____________ provides a means for combining subjectively determined prior probabilities with probabilities obtained by other means to obtain revised, or posterior, probabilities.

Bayes' theorem

_____________ Method: Assigning probabilities based on the assumption of equally likely outcomes.

Classical

Number of ____________ of N objects taken n at a time: A second useful counting rule enables us to count the number of experimental outcomes when n objects are to be selected from a set of N objects.

Combinations

The _______________ of events A and B is denoted by A∩B.

intersection

Number of _______________ of N Objects Taken n at a Time: A third useful counting rule enables us to count the number of experimental outcomes when n objects are to be selected from a set of N objects, where the order of selection is important.

Permutations

_________________ is a numerical measure of the likelihood that an event will occur.

Probability

___________ ______________ Method: Assigning probabilities based on experimentation or historical data.

Relative Frequency

_____________ Method: Assigning probabilities based on judgment.

Subjective

If P(A) = .75, P(A ∪ B) = .86, and P(A ∩ B) = .56, then P(B) = a. .67 b. .56 c. .11 d. .25

a. .67

The range of probability is _____, a. 0 to 1, inclusive b. any value between -1 to 1 c. any value between minus infinity to plus infinity d. any value larger than 0

a. 0 to 1, inclusive

Suppose we flip a fair coin five times and each time it lands heads up. The probability of landing heads up on the next flip is _____. a. 1/2 b. 1 c. 0 d. None of these answers are correct.

a. 1/2

The "Top Three" at a racetrack consists of picking the correct order of the first three horses in a race. If there are 10 horses in a particular race, how many "Top Three" outcomes are there? a. 720 b. 302,400 c. 10 d. 1,814,400

a. 720

Each customer entering a department store will either buy or not buy some merchandise. An experiment consists of following three customers and determining whether or not they purchase any merchandise. The number of sample points in this experiment is _____. a. 8 b. 6 c. 2 d. 4

a. 8

On a December day, the probability of snow is .30. The probability of a "cold" day is .50. The probability of snow and a "cold" day is .15. Are snow and "cold" weather independent events? a. yes b. no c. only when they are also mutually exclusive d. only if given that it snowed

a. yes

The __________ law provides a way to compute the probability of event A, or B, or both A and B occurring. The law is written as: P(A∪B) = P(A) + P(B) −P(A∩B)

addition

If P(A) = .62, P(B) = .56, and P(A ∪ B) = .70, then P(B | A) = _____. a. .9032 b. .4800 c. .7742 d. Not enough information is given to answer this question.

b. .4800

If A and B are mutually exclusive events with P(A) = .3 and P(B) = 0.5, then P(A ∩ B) = a. .20 b. 0 c. .30 d. .15

b. 0

Of five letters (A, B, C, D, and E), two letters are to be selected at random. How many possible selections are there? a. 20 b. 10 c. 7 d. 5!

b. 10

When the assumption of equally likely outcomes is used to assign probability values, the method used to assign probabilities is referred to as the _____. a. relative frequency method b. classical method c. subjective method d. probability method

b. classical method

You roll a fair six-sided die with the hopes of rolling a 5 or a 6. These two events are ___________ because they have no sample points in common. a. complements b. mutually exclusive events c. posterior events d. independent events

b. mutually exclusive events

The sample space refers to _____. a. the sample size minus 1 b. the set of all possible experimental outcomes c. any particular experimental outcome d. both any particular experimental outcome and the set of all possible experimental outcome

b. the set of all possible experimental outcomes

A graphical device used for enumerating sample points in a multiple-step experiment is a _____. a. bar chart b. tree diagram c. histogram d. None of these answers are correct.

b. tree diagram

If A and B are independent events with P(A) = .05 and P(B) = .65, then P(A | B) = _____. a. .8 b. .0325 c. .05 d. .65

c. .05

If A and B are independent events with P(A) = .4 and P(B) = .6, then P(A ∩ B) = _____. a. .76 b. 1 c. .24 d. .2

c. .24

If A and B are independent events with P(A) = .4 and P(B) = .25, then P(A ∪ B) = _____. a. .65 b. .10 c. .55 d. Not enough information is given to answer this question.

c. .55

Which of the following statements is always true? a. P(A) + P(B) = 1 b. −1 ≤ P(Ei) ≤ 1 c. P(A) = 1 − P(Ac) d. both P(A) = 1 − P(Ac) and P(A) + P(B) = 1

c. P(A) = 1 − P(Ac)

In an experiment, events A and B are mutually exclusive. If P(A) = .6, then the probability of B _____. a. can be any value between 0 and 1 b. can be any value greater than .6 c. cannot be larger than .4 d. Cannot be determined with the information given.

c. cannot be larger than .4

When the results of experimentation or historical data are used to assign probability values, the method used to assign probabilities is referred to as the _____. a. classical method b. subjective method c. relative frequency method d. posterior method

c. relative frequency method

The _______________ of event A is defined to be the event consisting of all sample points that are not in A.

complement

The probability of an event given that another event has occurred is called a _____________ probability. The conditional probability of A given B is denoted by P(A|B).

conditional

An experiment consists of four outcomes with P(E1) = .2, P(E2) = .3, and P(E3) = .4. The probability of outcome E4 is _____. a. .500 b. .024 c. .900 d. .100

d. .100

If A and B are independent events with P(A) = .2 and P(B) = .6, then P(A ∪ B) = _____. a. .12 b. .60 c. .62 d. .68

d. .68

If X and Y are mutually exclusive events with P(X) = .295, P(Y) = .32, then P(X ∪ Y) = _____. a. 1 b. .615 c. .094 d. 0

d. 0

Assume your favorite football team has two games left to finish the season. The outcome of each game can be win, lose, or tie. The number of possible outcomes is _____. a. 6 b. 2 c. 4 d. 9

d. 9

If P(A) = .5 and P(B) = .5, then P(A ∩ B) _____. a. is 0 b. is 1 c. is .25 d. Cannot be determined from the information given.

d. Cannot be determined from the information given.

A method of assigning probabilities based upon judgment is referred to as the _____. a. probability method b. classical method c. relative frequency method d. None of these answers are correct.

d. None of these answers are correct.

A magician holds a standard deck of cards and draws one card. The probability of drawing the ace of diamonds is 1/52. What method of assigning probabilities was used? a. subjective method b. objective method c. experimental method d. classical method

d. classical method

If one mutually exclusive event is known to occur, the other cannot occur; thus, the probability of the other event occurring is reduced to zero (and they are therefore ______________).

dependent

An _________ is a collection of sample points.

event

An __________ is any process that generates well-defined outcomes.

experiment

Basic Requirements for Assigning Probabilities: 1. The probability assigned to each experimental outcome must be between 0 and 1, _______________. 0 <P(Ei) <1 for all i where: Ei is the ith experimental outcome P(Ei) is its probability

inclusively

If the probability of event A is not changed by the existence of event B, we would say that events A and B are ________________.

independent

The ___________ of events A and B is the set of all sample points that are in both A and B.

intersection