Bstat ch 4

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A contingency table is a tabular summary of probabilities concerning two sets of complementary
events.

true

An event is a collection of sample space outcomes.

true

Two events are independent if the probability of one event is influenced by whether or not the other
event occurs.

falso

Mutually exclusive events have a nonempty intersection.

false

A subjective probability is a probability assessment that is based on experience, intuitive judgment, or
expertise.

true

The probability of an event is the sum of the probabilities of the sample space outcomes that
correspond to the event.

true

If events A and B are mutually exclusive, then P(A|B) is always equal to zero.

true

If events A and B are independent, then P(A|B) is always equal to zero.

false

If events A and B are mutually exclusive, then P(A]B) is always equal to zero.

true

Events that have no sample space outcomes in common, and, therefore cannot occur simultaneously
are referred to as independent events.

false

Two mutually exclusive events having positive probabilities are ______________ dependent.

always

___________________ is a measure of the chance that an uncertain event will occur.

Probability

A manager has just received the expense checks for six of her employees. She randomly distribute
the checks to the six employees. What is the probability that exactly five of them will receive the
correct checks (checks with the correct names)?

0

In which of the following are the two events A and B, always independent?

B and D.

If two events are independent, we can _____ their probabilities to determine the intersection
probability.

multiply

Events that have no sample space outcomes in common, and therefore, cannot occur simultaneously
are:

Mutually Exclusive

If events A and B are independent, then the probability of simultaneous occurrence of event A and
event B can be found with:

All of the above are correct

The set of all possible experimental outcomes is called a(n):

sample space

A ____________ is the probability that one event will occur given that we know that another event
already has occurred.

Conditional probability

The _______ of two events X and Y is another event that consists of the sample space outcomes
belonging to either event X or event Y or both event X and Y.

Union

If P(A) > 0 and P(B) > 0 and events A and B are independent, then:

P((A|B)) = P(A)

P(A U B) = P(A) + P(B) - P(A B) represents the formula for the

addition rule

A(n) _____ is the set of all of the distinct possible outcomes of an experiment.

Sample Space

The _____ of an event is a number that measures the likelihood that an event will occur when an
experiment is carried out.

Probability

When the probability of one event is influenced by whether or not another event occurs, the events are
said to be _____.

Dependent

A process of observation that has an uncertain outcome is referred to as a(n) _____.

Experiment

When the probability of one event is not influenced by whether or not another event occurs, the events
are said to be _____.

Independent

A probability may be interpreted as a long run _____ frequency.

Relative

If events A and B are independent, then P(A|B) is equal to _____.

P(A)

The simultaneous occurrence of event A and B is represented by the notation: _______.

AnB

A(n) _______________ probability is a probability assessment that is based on experience, intuitive
judgment, or expertise.

Subjective

A(n) ______________ is a collection of sample space outcomes

event

Probabilities must be assigned to experimental outcomes so that the probabilities of all the
experimental outcomes must add up to ___.

1

Probabilities must be assigned to experimental outcomes so that the probability assigned to each
experimental outcome must be between ____ and ____ inclusive.

0 and 1

The __________ of event X consists of all sample space outcomes that do not correspond to the
occurrence of event X.

Complement

The _______ of two events A and B is another event that consists of the sample space outcomes
belonging to either event A or event B or both event A and B.

Union

The _______ of two events A and B is the event that consists of the sample space outcomes belonging
to both event A and event B.

intersection

What is the probability of rolling a seven with a pair of fair dice?

6/36

What is the probability of rolling a value higher than eight with a pair of fair dice?

10/36

What is the probability that an even number appears on the toss of a die?

0.5

What is the probability that a king appears in drawing a single card form a deck of 52 cards?

1/13

If we consider the toss of four coins as an experiment, how many outcomes does the sample space
consist of?

16

What is the probability of at least one tail in the toss of three fair coins?

7/8

A lot contains 12 items, and 4 are defective. If three items are drawn at random from the lot, what is
the probability they are not defective?

0.2545

A person has dealt 5 cards from a deck of 52 cards. What is the probability they are all clubs?

0.0005

A group has 12 men and 4 women. If 3 people are selected at random from the group, what is the
probability that they are all men?

0.3929

Container 1 has 8 items, 3 of which are defective. Container 2 has 5 items, 2 of which are defective. I
one item is drawn from each container:

What is the probability that both items are not defective?

A. 0.3750

Container 1 has 8 items, 3 of which are defective. Container 2 has 5 items, 2 of which are defective. If
one item is drawn from each container:

What is the probability that the item from container one is defective and the item from container 2 is
not defective?

0.2250

Container 1 has 8 items, 3 of which are defective. Container 2 has 5 items, 2 of which are defective. If
one item is drawn from each container:

What is the probability that one of the items is defective?

0.4500

A coin is tossed 6 times. What is the probability that at least one head occurs?

63/64

Suppose P(A) = .45, P(B) = .20, P(C) = .35, P(E|A) = .10, P(E|B) = .05, and P(E|C) = 0. What is P(E)?

.055

Suppose P(A) = .45, P(B) = .20, P(C) = .35, P(E|A) = .10, P(E|B) = .05, and P(E|C) = 0. What is P(A
E)?

.818

Suppose P(A) = .45, P(B) = .20, P(C) = .35, P(E|A) = .10, P(E|B) = .05, and P(E|C) = 0. What is P(B|
E)?

.182

Suppose P(A) = .45, P(B) = .20, P(C) = .35, P(E|A) = .10, P(E|B) = .05, and P(E|C) = 0. What is P (
E)?

0

Given the standard deck of cards, what is the probability of drawing a red card, given that it is a face
card?

.5

Given a standard deck of cards, what is the probability of drawing a face card, given that it is a red
card?

.231

A machine is made up of 3 components: an upper part, a mid part, and a lower part. The machine is
then assembled. 5 percent of the upper parts are defective; 4 percent of the mid parts are defective; 1
percent of the lower parts are defective. What is the probability that a machine is non-defective?

.903

A machine is produced by a sequence of operations. Typically one defective machine is produced per
1000 parts. What is the probability of two non-defective machines being produced?

0.998

A pair of dice is thrown. What is the probability that one of the faces is a 3, given that the sum of the
two faces is 9?

1/4

A card is drawn from a standard deck. What is the probability the card is an ace, given that it is a
club?

1/13

A card is drawn from a standard deck. Given that a face card is drawn, what is the probability it will
be a king?

1/3

Independently a coin is tossed, a card is drawn from a deck, and a die is thrown. What is the
probability of observing a head on the coin, an ace on the card, and a five on the die?

.0064

A family has two children. What is the probability that both are girls, given that at least one is a girl?

1/3

What is the probability of winning four games in a row, if the probability of winning each game
individually is 1/2

1/16

At a college, 70 percent of the students are women and 50 percent of the students receive a
grade of C. 25 percent of the students are neither female nor C students. Use this contingency

.45

At a college, 70 percent of the students are women and 50 percent of the students receive a
grade of C. 25 percent of the students are neither female nor C students. Use this contingency

.25

At a college, 70 percent of the students are women and 50 percent of the students receive a
grade of C. 25 percent of the students are neither female nor C students. Use this contingency

.17

At a college, 70 percent of the students are women and 50 percent of the students receive a
grade of C. 25 percent of the students are neither female nor C students. Use this contingency

If the student has received a grade of C, what is the probability that he is male?

0.10

At a college, 70 percent of the students are women and 50 percent of the students receive a
grade of C. 25 percent of the students are neither female nor C students. Use this contingency

0.90

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