Deck 9: Introduction to Probability and Statistics

Question 1

A manufacturer places a four-symbol code on each unit of a product.The first three symbols are numbers with the first not 0,and the fourth symbol is a letter other than o.How many codes are possible?

Answer 1

22,500

Question 2

The value of is

A) 30
B) 70
C) 120
D) 720
E) 75,600

Answer 2

720

Question 3

Determine the value of
and simplify your answer.

Answer 3

60

Question 4

Determine

Question 5

Determine

Question 6

A certain state has license plates that consist of 3 letters followed by 4 numerals.How many different types of license plate can be made?

Question 7

Determine the value of
and simplify your answer.

Question 8

A club has ten members.In how many ways can the offices of president,vice president,secretary,and treasurer be filled if no member can serve in two offices?

A) 10,000
B) 5040
C) 210
D) 40
E) 16

Question 9

From a group of 12 people,in how many ways can the offices of chairperson,secretary,and treasurer be filled by three different people?

Question 10

A building contractor can order lumber from 5 suppliers,bricks from 4 suppliers,and hardware from 8 suppliers.If the contractor chooses one supplier for each item,how many choices are available for the three items?

A) 17
B) 120
C) 160
D) 320
E) 4,096,000

Question 11

In how many ways is it possible to answer a five-question multiple-choice examination if each question has three choices and exactly one choice is selected for each question?

Question 12

The number of ways in which a student can answer an eight-question true-false examination is

A) 8
B) 16
C) 64
D) 256
E) 40,320

Question 13

At a restaurant a complete dinner consists of a salad,an entree,a dessert,and a beverage.For the salad,the choices are tossed green salad,gelatin salad,or cottage cheese; for the entree,the choices are chicken,roast beef,or flounder; for the dessert,the choices are pudding,pie,cake,or ice cream; for the beverage,the choices are coffee,tea,or milk.How many complete dinners are possible?

Question 14

A college mathematics club of 30 students needs to elect new officers.If there are 3 positions available and no one can serve in more than one position,how many different slates of candidates are possible?

Question 15

A math instructor has twelve students in his class.It so happens that he has exactly 12 desks in his classroom.How many ways can the 12 students be arranged in the 12 desks?

Question 16

In how many ways can a basketball coach assign the five different positions to her eight-member team if all members are equally qualified at all positions?

Question 17

In how many ways is it possible to answer a six-question true-false examination.

Question 18

Five different books are to be arranged horizontally on a bookshelf.(a)In how many ways can this be done? (b)If two are mathematics books and three are accounting books,in how many ways can all the books be arranged if the first two books are to be in mathematics?

Question 19

If a basketball league has five teams,how many different end-of-the-season rankings are possible? Assume that there are no ties.

Question 20

In a certain state,all drivers are given a driver's license code consisting of 2 letters followed by 6 numerals.How many different drivers license codes are possible?

Question 21

The value of is

A) 90.
B) 45.
C) 40.
D) 36.
E)

Question 22

The value of is

A) 18.
B) 36.
C) 72.
D) 5040.
E) 181,440.

Question 23

How many distinguishable horizontal arrangements of all the letters in BOOKS are possible?

Question 24

A company will hire five people: three for the assembly department and two for the finishing department.There are eight applicants who are equally qualified to work in each department.In how many ways can the company fill the positions?

Question 25

How many different two-card hands can be dealt from an ordinary deck of 52 playing cards?

Question 26

In how many ways can a four-member committee be selected from a group of seven people?

Question 27

Determine the value of
∙
and simplify your answer.

Question 28

From a committee of five men and four women,a subcommittee consisting of two men and two women is to be formed.In how many ways can the subcommittee be chosen?

Question 29

In a track race of 8 contestants,how many ways can the 1st,2nd,and 3rd places finishes happen?

Question 30

A youth sports team plays seven games.In how many ways can the outcomes of the games result in five wins and two losses?

Question 31

In a math course of 12 students,the instructor decides that he would like 4 students to go to the board to present 4 different problems to the class.The students go to the board one at a time.No student goes to the board more than once.How many ways can he choose the 4 students?

Question 32

The value of the product ∙
Is

A) 3.
B) 4.
C) 6.
D) 12.
E) 24.

Question 33

From a group of ten people,five are assigned to room A and two to room B.In how many ways can the assignment be made?

A) 15,120
B) 2520
C) 252
D) 45
E) 10

Question 34

The value of the sum +
Is

A) 0.
B) 4.
C) 6.
D) 8.
E) 12.

Question 35

The winner of a contest can choose any two of six different prizes.How many choices are possible?

A) 15
B) 20
C) 25
D) 30
E) 34

Question 36

Determine the value of
and simplify your answer.

Question 37

Determine the value of
and simplify your answer.

Question 38

From a lot of ten computers,two are selected for extensive testing.In how many ways can the selection be made?

Question 39

How many distinguishable horizontal arrangements of all the letters in LETTERS are possible?

A) 5040
B) 21
C) 2520
D) 120
E) 1260

Question 40

Determine the value of
∙
and simplify your answer.

Question 41

A grocery store displays 100 green peppers in 10 rows of 10 each.It is quite likely that customer A's choice of the 2 best peppers to buy would differ from customer B's choice,even if the peppers were more or less identical.In how many ways (sample points)could the first customer to see the green pepper array choose 2 peppers to buy?

Question 42

Determine

Question 43

How many distinguishable arrangements of all letters in the word MISSISSIPPI are possible?

Question 44

From an ordinary deck of 52 playing cards,a two-card hand is dealt.In how many ways can the two cards be of the same face value?

A) 2
B) 6
C) 78
D) 104
E) 1326

Question 45

In a 20-question examination,each question is worth 5 points and is graded right or wrong.Considering the individual questions,in how many ways can a student score 85 points or higher?

Question 46

Fourteen children from a day care center are the first to arrive at a movie theater that seats 600.They decide to pull a trick on their chaperons by hiding under the seats,one child per seat.If we consider the 14 seats selected to be one "hiding place",how many potential hiding places would the chaperons conceivably have to search? (Leave answer in factorial form.)

Question 47

A family has two children.Determine
(a)the event
that at least one child is a boy;
(b)the event
that at least one child is a girl.
(c)Are
and
mutually exclusive?

Question 48

From an urn that contains eight marbles numbered 1 through 8,three marbles are randomly selected in succession and the results observed.Determine the number of sample points in the sample space of this experiment if the marbles are selected
(a)with replacement and
(b)without replacement.

Question 49

If S =
is a sample space of an experiment with events

and
find


(d)Of the events E,F,and G,which pairs are mutually exclusive?

Question 50

If S =
is a sample space of an experiment with events

and
find



(e)Of the events E,F,and G,which pairs are mutually exclusive?

Question 51

If a die is rolled and then a coin is tossed,and the results are observed,determine the sample space of this experiment.

Question 52

In a math course of 12 students,the instructor decides that he would like 4 students to go to the board simultaneously to present 4 different problems to the class.How many ways can he choose the 4 students?

Question 53

If S = is a sample space of an experiment with events E =
And
Then E ∩ F' =

A)
B)
C)
D)
E)

Question 54

AN URN CONTAINS FOUR MARBLES,NUMBERS 1,2,3,AND 4.IF A MARBLE IS DRAWN AND THEN A COIN IS TOSSED,AND THE RESULTS are observed,determine the sample space of this experiment.

Question 55

A student must select two courses in the liberal arts and three courses in the social sciences.There are six liberal arts courses and ten social science courses,all of which are different,from which the student may choose.How many selections are possible?

A) 6
B) 135
C) 750
D) 1800
E) 21,600

Question 56

A coin is tossed three times.Determine
(a)the event
that exactly two heads occur;
(b)the event
that at least two heads occur;
(c)the event
that no head occurs.

Question 57

If S = is a sample space of an experiment with events E =
And
Then E ∪ F' =

A)
B)
C)
D)
E)

Question 58

A car rental agency buys 140 new tires to outfit its 35-vehicle fleet.The tires can be distinguished by their production serial numbers.Suppose the tire dealer delivers the tires and dumps them in a heap.The rental agency's maintenance person selects 4 tires from the heap to put on the first car.How many ways can she select the 4 tires to put on the car?

Question 59

Two light bulbs are selected from a box of 20 bulbs.For this experiment,how many sample points are in the sample space?

Question 60

Determine

Question 61

A family has 3 children,2 girls and a boy.Every morning (Tuesday through Saturday)each child selects a stock at random from the list printed in the newspaper.If the stock is up,that child does the morning dishes.If the stock is down,the child who picked the stock does the noon dishes.If the stock is unchanged,that child does the evening dishes.If there is a tie-2 children to do the noon dishes,for example-then both children work together to do the noon dishes,and the remaining meal's dishes are done by default by mom or dad.The assignments can be thought of as an ordered triple,ordered by age.For example,(+,0,-)means that the youngest does the morning dishes (the stock was up),the oldest child does the noon dishes (the stock was down),and the middle child,whose stock was unchanged,does the dishes after the evening meal.(-,0,0)means the youngest does the noon dishes,the other two work together on the dishes from the evening meal.The morning dishes are done by mom and dad.Determine the following events:
(a)
= {the oldest and youngest work together doing the dishes; the middle child does the dishes from a different meal}
(b)
= {the youngest child has the day off}
(c)
= {mom and dad do the dishes twice}
(d)
= {the oldest child does the noon dishes alone}
(e)
(f)
∪
(g)Let
= {either the oldest or the youngest child does the morning dishes alone}
Let
= {the middle child does the evening dishes alone}
∩
(h)
∩
(i)
∪
(j)
∩

Question 62

If P(E)= 0.3,P(F)= 0.4,
P(E ∩
F).
F)= 0.2, find P(E ∪

Question 63

Three fair coins are tossed.Find the probability that
(a)three tails show;
(b)exactly two tails show.

Question 64

A family is having a group picture taken to mail to all the relatives.Mother,Father,Son,and Daughter are being photographed,but somebody has to work the camera,so only 3 people at a time can be photographed.Last year's pictures looked "funny" for some reason,so this year they decide to sit next to each other in various orders to see which composition is best.Let the ordered 4-tuple (M,D,S,
B) represent the photographer (Mom here), the person on the left in the picture (Dad here), the person in the middle in the picture (the Sister, in this case), and the person sitting on the right (Brother here). Determine the following events:
(a) = {Dad, the tallest, sits in the middle}
(b) = {the photographer is male and Mom is on the left}
(c) = {there is only one female in the picture}
(d) = {Dad is to the immediate left of Mom}
(e)
(f) ∪
(g) ∩
(h) ∩
(i) ∪
(j) ∩

Question 65

An urn contains two red and three green marbles.Two marbles are randomly drawn in succession without replacement.Determine the probability that
(a)the first marble is red and the second is green;
(b)both marbles are red.

Question 66

An office worker spends each coffee break at the same deli.This deli has the same 8 varieties of coffee every day.To add variety and excitement to his or her day,the office worker decides to randomly choose a coffee variety in the morning and then randomly choose a variety in the afternoon.How many morning coffee - afternoon coffee choices are there?

Question 67

An urn contains ten marbles numbered 1 through 10.If a marble is randomly selected from the urn,determine the probability that it shows a number greater than or equal to 4.

Question 68

A card is randomly drawn from an ordinary deck of 52 playing cards.What is the probability that it is
(a)a king;
(b)not a heart;
(c)a 10 and not red.

Question 69

Two fair dice are rolled.What is the probability that the sum of the dots appearing is
(a)2;
(b)7?

Question 70

A man has a $1,a $5,a $10,and a $20 bill in his billfold.He also has a penny,a nickel,a dime,and a quarter in his pants pocket.He decides to treat himself by spending one bill and one coin.How many spending possibilities does he have?

Question 71

Two cards are randomly drawn with replacement from a standard deck of 52 playing cards.Find the probability that
(a)both cards are aces;
(b)the first card is red and the second card is a club;
(c)one card is red and the other is a club.

Question 72

A state has decided to issue personalized license plates with 3 letters on them.The original idea was that these letters would represent the vehicle owner's first,middle,and last initials,respectively.Unfortunately,some 3 letter combinations are more colorful than others and the state received requests for combinations that in no way resembled the person's initials.The Department of Motor Vehicles decided to withdraw inappropriate or suggestive combinations.How long was the list of personalized plates that had to be reviewed?

Question 73

A man has a $1,a $5,a $10,and a $20 bill in his billfold.He also has a penny,a nickel,a dime,and a quarter in his pants pocket.He decides to treat himself by spending one bill and one coin.Determine the following events.
(a)
= { the amount of money the man is prepared to spend,expressed in cents,is a prime number}
(b)
= {the amount of money the man is prepared to spend is more than one third of all the money he is carrying}
(c)
= {the man spends the nickel}
(d)
= {the amount to be spent is one half the amount to be spent under another selection}
(e)
(f)
∪
(g)
∩
(h)
∩
(i)
∪
(j)
∩

Question 74

A fair coin is tossed and then a fair die is rolled.Determine the probability that
(a)a head and an odd number show;
(b)a 2 or 4 shows.

Question 75

If the probability that a certain horse wins a race is
,find the odds that this event occurs.

Question 76

A plane flies from New York to Chicago,from Chicago to Denver,and from Denver to Los Angeles.The plane's on-time,late,or early departure from each city is recorded as 0 or - or +,respectively.For example,(+,-,0)represents the plane leaving earlier than its scheduled departure time from New York,later than its scheduled departure time from Chicago,and on-time from Denver.Assume that the time ahead of schedule or behind schedule is the same so that the pilot can make up for a late departure.For example,(-,0,+)means the plane was x minutes late out of New York,on-time out of Chicago,and made up the x minutes late out of New York by leaving Denver x minutes early.The plane is,therefore,on time when it arrives in Los Angeles.Determine the following events:
(a)
= {the plane arrives in L.A.on time}
(b)
= {the plane is late on arrival in L.A.}
(c)
= {the plane is on time when it arrives at Denver}
(d)
= {the plane arrives in L.A.as late as possible}
(e)
(f)
∪
(g)
∩
(h)
∩
(i)
∪
(j)
∩

Question 77

A state legislative body is considering an action that allows gambling within the state.An opinion survey of 200 voters was conducted and the results are indicated in the following table:
Favor Oppose No Opinion Total
Democrat 40 35 9 84
Republican 60 30 6 96
Other 4 8 8 20
Total 104 73 23 200
Assume that the survey reflects the opinion of the voting population.If a person is selected at random,determine each of the following (empirical)probabilities:
(a)P (opposes gambling)
(b)P (Republican)
(c)P (Democrat who favors gambling).

Question 78

If a pair of dice are rolled,the probability that the sum of the numbers of dots appearing is 5 is

A)
B)
C)
D)
E)

Question 79

An urn contains ten marbles numbered 1 through 10.If two marbles are randomly drawn in succession without replacement,determine the probability that
(a)the first marble drawn shows 1 and the second shows 2;
(b)both show an odd number;
(c)at least one marble shows a number greater than 5.

Question 80

A United Nations diplomat can travel from Washington,D.C.to New York City in 6 ways.Depending on the urgency of the trip,she can fly by helicopter,fly by plane,drive the car to a suburban subway station and then take the subway the rest of the way,drive by limousine,take the train,or borrow a friend's yacht and sail most of the way.When she returns to Washington,D.C.,the same modes of transportation are available.How many round trip transportation combinations are available to her?