BANA 2372 - Chapter 4 - Midterm Exam 1 - Practice

Most states run a lottery game in which players may select a three digit number, then later that day a televised drawing randomly selects a winning three digit number. Suppose you select one three digit number and buy a ticket. What is the probability that your three digit number is an exact match with the winning three digit number?

1/1000

An experiment consists of rolling two fair six-sided dice and finding the sum of the spots. How many outcomes are in the sample space? What is the probability of rolling a sum of 12?

1/36

A board of directors consists of eight men and four women. A four-member search committee is to be chosen at random to recommend a new company president. What is the probability that all four members of the search committee will be women?

1/495 or 0.002

Of five letters (A, B, C, D, and E), two letters are to be selected at random. How many possible selections are there?

10

A national pollster has developed 15 questions designed to rate the performance of the Prime Minister of Canada. The pollster will select 10 of these questions. How many different arrangements are there for the order of the 10 selected questions?

10,897,286,400

Most states run a lottery game in which players may select a three digit number, then later that day a televised drawing randomly selects a winning three digit number. How many outcomes are in the sample space?

1000

An overnight express company must include five new cities on its routes. How many different routes possible, assuming that it does not matter in which order the cities are included in the routing?

120

From a group of six people, two individuals are to be selected at random. How many possible selections are possible?

15

An experiment consists of selecting a student body president and vice president. All undergraduate students (freshmen through seniors) are eligible for these offices. How many sample points (possible outcomes as to the classifications) exist?

16

Each customer entering a department store will either buy or not buy some merchandise. An experiment consists of following 4 customers and determining whether or not they purchase any merchandise. How many sample points exist in the above experiment? (Note that each customer is either a purchaser or non-purchaser.)

16

Consider the experiment of flipping a coin four times. How many outcomes are in the sample space? If needed, create a tree diagram to help answer the question.

16 - this experiment consists of two possible outcomes (Heads or Tails) for each of the four flips. Therefore, the number of outcomes in the sample space is 24 = 16.

Assuming that each of the 52 cards in an ordinary deck has a probability of 1/52 of being drawn, what is the probability of drawing a black ace?

2/52

The National Centre for Health Statistics reported that of every 883 deaths in recent years, 24 resulted from an automobile accident, 182 from cancer and 333 from heart disease. Using the relative frequency approach, what is the probability that a particular death is due to an automobile accident?

24/883 or 0.027

Assume your favorite football team has 3 games left to finish the season. The outcome of each game can be win, lose, or tie. How many possible outcomes exist?

27

A representative of the Environmental Protection Agency wants to select samples from 5 landfills. The Director has 10 landfills from which to collect samples. How many different samples are possible?

30,240

In a particular course, it was determined that only 70% of the students attend class on Fridays. From past data, it was noted that 95% of those who went to class on Fridays passed the course, while only 10% of those who did not go to class on Fridays passed the course. If a student passes the course, what is the probability that the student did not attend on Fridays?

4.3%

In a particular course, it was determined that only 70% of the students attend class on Fridays. From past data, it was noted that 95% of those who went to class on Fridays passed the course, while only 10% of those who did not go to class on Fridays passed the course. What percent of students can be expected to pass the course?

69.5%

If A and B are independent and P(A) = .5 and P(B) = .5, then P(A ∪ B) is:

75 .5 + .5 - (.5 . .5) = .75

Each customer entering a department store will either buy or not buy some merchandise. An experiment consists of following 3 customers and determining whether or not they purchase any merchandise. The number of sample points in this experiment is

8

Three applications for admission to a local university are checked, and it is determined whether each applicant is male or female. The number of sample points in this experiment is

8

Assume your favorite football team has 2 games left to finish the season. The outcome of each game can be win, lose or tie. The number of possible outcomes is

9

Suppose that of all college graduates, 80% choose their particular profession because they believe the work will be fulfilling, 50% believe they can achieve a high salary, and 40% believe they will have both. What is the probability that a college graduate chooses his particular profession because he believes that the work will be fulfilling, he believes that he can achieve a high salary, or both?

90% 0.8 + 0. 5 - 0.4 = 0.9 or 90%

Which of the following graphical displays is helpful when using Bayes' theorem to calculate a probability?

A tree diagram

Which of the following statements about an event and its complement is false?

An event and its complement are always independent.

The union of two events A and B can always be denoted by

AꓴB

The union of two events A and B can always be denoted by: events A and B can always be denoted by:

AꓴB

An experiment consists of four outcomes with P(E1) = .2, P(E2) = .3, and P(E3) = .4. The probability of outcome E4 is

.1

Given the information below, find P(S ∩ W). Cell Phone Service Provider County Sprint (S) AT&T (A) Verizon (V) Row Total Macomb (M) 17 25 8 50 Oakland (O) 19 38 13 70 Wayne (W) 24 37 19 80 Col Total 60 100 40 200

.12

If P(AB) = 0.40 and P(B) = 0.30, find P(A ∩ B).

.120

Suppose the probability of finding a job prior to graduation is .76. Also suppose that the probability of being promoted within the first year, given that you found a job prior to graduation, is .25. What is the probability of finding a job prior to graduation and being promoted within the first year?

.19

Given the information below, find P(V). Cell Phone Service Provider County Sprint (S) AT&T (A) Verizon (V) Row Total Macomb (M) 17 25 8 50 Oakland (O) 19 38 13 70 Wayne (W) 24 37 19 80 Col Total 60 100 40 200

.20

Given the information below, find P(V |W). Cell Phone Service Provider County Sprint (S) AT&T (A) Verizon (V) Row Total Macomb (M) 17 25 8 50 Oakland (O) 19 38 13 70 Wayne (W) 24 37 19 80 Col Total 60 100 40 200

.2375

A used-car salesman has kept records on the customers who visited his showroom. Thirty percent of the people who visited his showroom were female. Furthermore, his records show that 35% of the females who visited his showroom made a purchase, while 20% of the males who visited his showroom made a purchase. What is the probability that a customer entering his showroom will make a purchase?

.245

If A and B are independent and P(A) = .5 and P(B) = .5, then P(A ∩ B) is:

.25.

Assume you have applied for two jobs A and B. Getting an offer for job A has no influence on whether or not you receive an offer for job B and vice versa. The probability that you get an offer for job A is .51. The probability of being offered job B is .33. What is the approximate probability that you do not get either job?

.328 P(Ac).P(Bc) = (0.49)(0.67) = .328

If A and B are independent and P(A)=.5, then P(A | B) is:

.50

If a fair coin is tossed 10 times and landed heads up each of those 10 times, what is the probability that it will land tails up on the 11th toss?

.50

If A and B are independent and P(A) = .5 and P(B) = .5, then P(A | B) is:

.50.

Suppose A and B are independent events with P(A) = .35 and P(B) = .20. Calculate P(A^c∩B^c)

.52

A used-car salesman has kept records on the customers who visited his showroom. Thirty percent of the people who visited his showroom were female. Furthermore, his records show that 35% of the females who visited his showroom made a purchase, while 20% of the males who visited his showroom made a purchase. Suppose we were told that a customer just made a purchase. What is the probability that the customer was a male?

.57

The manager of PayALot Drug Store knows that 30% of the customers entering the store buy prescription drugs, 60% buy over-the-counter drugs, and 18% buy both types of drugs. What is the probability that a randomly selected customer will buy either one or the other of these two types of drugs?

.72

IF A and B are independent and P(A)=.5 and P(B)=.5, then P(A u B) is:

.75

Suppose you flip two fair coins. What is the probability that you get at least one tail?

.75

The results of a survey of 800 married couples and the number of children they had are shown below. No. of Children Probability 0 .050 1 .125 2 .600 3 .150 4 .050 5 .025 If a couple is selected at random, what is the probability that the couple will have at least two children?

.825

Suppose you owned a trick six-sided die in which the outcomes had the following long-term probabilities: Outcome Probability 1 .05 2 .15 3 .30 4 ,30 5 .05 6 .15 What is the probability of rolling an even number or a multiple of 3?

.90

Suppose P(A) = .50 and P(B) = .30. If A and B are mutually exclusive, what is P(A ∩ B)?

0

If P(A) = 0.48, P(A ∪ B) = 0.82, and P(B) = 0.54, then P(A ∩ B) =

0.2000

If P(A) = 0.45, P(B) = 0.55, and P(A ∪ B) = 0.78, then P(A B) =

0.40

If A and B are independent events with P(A) = 0.65 and P(A ∩ B) = 0.26, then, P(B) =

0.400

If P(A) = 0.4, P(B | A) = 0.35, P(A ∪ B) = 0.69, then P(B) =

0.43

Given that event E has a probability of 0.31, the probability of the complement of event E

0.69

Events A and B are mutually exclusive with P(A) = 0.3 and P(B) = 0.2. Then, P(Bc) =

0.8

If A and B are mutually exclusive events with P(A) = 0.3 and P(B) = 0.5, then P(A ∪ B) =

0.8

If each of two independent file servers has a reliability of 93% and either alone can run the web site, then the overall web site availability is

0.9951

Which approach to probability is exemplified by the following formula?

Empirical approach

A graphical device used for enumerating sample points in a multiple-step experiment is a

None of these alternatives is correct.

If two events, A and B, are independent, then:

None of these alternatives is correct.

Independent events A and B would be consistent with which of the following statements:.

P (A) = .4, P (B) = .5, P (A ∩ B) = .2

Events A and B are mutually exclusive. Which of the following statements is also true?

P(A ∪ B) = P(A) + P(B)

A recent survey finds that 78% of people spend an average of at least 30 minutes per day surfing the internet while they are at work. Let A = Spending an average of at least 30 minutes each day surfing the internet while at work. Which of the following is the complement of A?

Spending an average of less than 30 minutes per day surfing the internet while at work.

In statistical experiments, each time the experiment is repeated

a different outcome may occur

In statistical experiments, each time the experiment is repeated:

a different outcome might occur.

A graphical method of representing the sample points of an experiment is

a tree diagram

A counseling agency has the following data on the gender and marital status of 200 clients: Male Female Single 20 30 Married 100 50 a. If the client was a male, what is the probability that he is single? b. Calculate the probability that a client is female. Calculate the probability that the client is female given that she is married. Are the two events (being a female and being married) dependent or independent? Explain.

a. .17 b. The events are dependent because the calculated probabilities differ.

A small town has 5600 residents. The residents in the town were asked whether or not they favored building a new bridge across the river. You are given the following information on the residents' responses, broken down by sex. Men Women In Favor 1400 280 Opposed 840 3080 a. What is the probability that a randomly selected resident is in favor of building the bridge? b. What is the probability that a randomly selected resident is a woman? c. What is the probability that a randomly selected resident is a man and is in favor of building the bridge?

a. .30 b. .60 c. 25

The union of events A and B is the event containing

all the sample points belonging to A or B or both

Any process that generates well-defined outcomes is

an experiment

Let A = Roll a 2 on a fair six-sided die. Let B = Do not roll a 2 on a fair six-sided die. Events A and B are:

both mutually exclusive and complementary.

Two events with nonzero probabilities:

can not be both mutually exclusive and independent

In an experiment, events A and B are mutually exclusive. If P(A) = 0.6, then the probability of B

cannot be larger than 0.4

A method of assigning probabilities which assumes that the experimental outcomes are equally likely is referred to as the

classical method

When the assumption of equally likely outcomes is used to assign probability values, the method used to assign probabilities is referred to as the

classical method

The counting rule that is used for counting the number of experimental outcomes when n objects are selected from a set of N objects where order of selection is not important is called

combination

The counting rule that is used for counting the number of experimental outcomes when n objects are selected from a set of N objects where the order of selection is not important is called the:

counting rule for combinations

The counting rule that is used for counting the number of experimental outcomes when n objects are selected from a set of N objects where order of selection is important is called the:

counting rule for permutations.

Two events are mutually exclusive

if they have no sample points in common

Two events are mutually exclusive:

if they have no sample points in common

A sample point refers to the

individual outcome of an experiment

The intersection of two mutually exclusive events

must always be equal to 0

The intersection of two mutually exclusive events:

must always be equal to 0

The counting rule that is used for counting the number of experimental outcomes when n objects are selected from a set of N objects where order of selection is important is called

permutation

Bayes' theorem is used to compute

posterior probabilities of an event and its complement.

Bayes' theorem is used to compute:

posterior probabilities of an event and its complement.

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

relative frequency method

Posterior probabilities are:

revised probabilities of events based on additional information

Each individual outcome of an experiment is called

sample point

A method of assigning probabilities based upon judgment is referred to as the

subjective method

A method of assigning probabilities based upon judgment is referred to as the:

subjective method.

The collection of all possible sample points in an experiment is

the sample space

The set of all possible sample points (experimental outcomes) is called

the sample space

The collection of all possible sample points in an experiment is:

the sample space.

The set of all possible outcomes of an experiment is:

the sample space.

The sample space refers to

the set of all possible experimental outcomes

The probability of any event is:

the sum of the probabilities of the sample points in the event.

The probability of any two event is

the sum of the probabilities of the sample points in the event.

The addition law is potentially helpful when we are interested in computing the probability of:

the union of two events.

Two events are complementary (i.e., they are complements) if

they are disjoint and their probabilities sum to one.

A graphical representation that helps in visualizing a multiple-step experiment is called a:

tree diagram.

The range of probability is

zero to one

The range of values for a probability is:

zero to one.