65)
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.
65)
66)
A youth sports team plays seven games. In how many ways can the outcomes of the
games result in five wins and two losses?
66)
67)
How many different two–card hands can be dealt from an ordinary deck of 52 playing
cards?
67)
68)
Determine 14C10
68)
69)
Ten tickets numbered from 1 to 10 are placed in a hat. If two tickets are randomly drawn
with replacement, find the probability the sum is 15.
69)
70)
If the probability that a certain horse wins a race is 1
4, find the odds that this event occurs.
70)
71)
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.
71)
72)
In a survey of newspaper readers, it was found that 40% like the Gazette, 25% liked the
Bulletin, and 10% liked both. If a person in the survey is randomly selected, find the
probability that the person liked the Bulletin, given that he or she liked the Gazette.
72)
73)
If two cards are randomly drawn, without replacement, from a standard deck of 52 cards,
find the probability that the second card is not a jack or queen, given that the first card is a
jack or queen.
73)
74)
Urn I contains two red and three white marbles, and Urn II contains three red and four
white marbles. A marble is randomly drawn from Urn I and placed into Urn II. A marble is
then randomly drawn from Urn II. Find the probability that it is red.
74)
75)
The probability that Bob survives ten more years is 4
5, and the probability that Mary
survives ten more years is 5
6. Find the probability that exactly one of them survives ten
more years. (Assume independence.)
75)
76)
A coin is tossed three times. Determine
(a) the event E1 that exactly two heads occur;
(b) the event E2 that at least two heads occur;
(c) the event E3 that no head occurs.
76)
77)
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?
77)
78)
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?
78)
79)
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.
79)
80)
An urn contains 3 green, 2 yellow, and 6 red marbles. If two marbles are randomly drawn
without replacement, find the probability the second one is yellow, given that the first
marble drawn is red.
80)
81)
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?
81)
82)
A quiz contains four multiple–choice problems. Each problem has five choices for the
answer, but only one of them is correct. If a student randomly guesses the answer to each
problem, find the probability that the student gets exactly three correct answers.
82)
83)
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?
83)
84)
If a fair die is rolled three times, find the probability that a 3 or 5 comes up each time.
84)
85)
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.
85)
86)
Two cards are randomly drawn with replacement from a standard deck of 52 cards. Find
the probability of drawing, in order, the queen of hearts and a diamond.
86)
87)
How many distinguishable arrangements of all letters in the word MISSISSIPPI are
possible
87)
88)
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?
88)
89)
If P(E) = 0.3, P(F) = 0.4, and P(EF)= 0.2, find P(EF).
89)
90)
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?
90)
91)
An urn contains five chips numbered from 1 to 5. A chip is randomly drawn. Let E be the
event of drawing a 3 and F be the event of drawing a 5. Are E and F independent?
91)
92)
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?
92)
93)
A family has two children. Determine
(a) the event E1 that at least one child is a boy;
(b) the event E2 that at least one child is a girl.
(c) Are E1 and E2 mutually exclusive?
93)
94)
Determine the value of 10C8 and simplify your answer.
94)
95)
Determine the value of 6P2 and simplify your answer.
95)
96)
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) E1= { the amount of money the man is prepared to spend, expressed in cents, is a
prime number}
(b) E2= {the amount of money the man is prepared to spend is more than one third of all
the money he is carrying}
(c) E3= {the man spends the nickel}
(d) E4= {the amount to be spent is one half the amount to be spent under another
selection}
(e) E‘2
(f) E3E4
(g) E3E4
(h) E1E4
(i) E1E‘1
(j) E1E‘1
96)
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. Find the requested probability.
97)
The plane is on time at L.A., when it left New York on time but left Chicago later than
scheduled.
97)
98)
If events E and F are independent with P(E) = 0.3 and P(F) = 0.5, find P(E‘ F).
98)
99)
From a group of 12 people, in how many ways can the offices of chairperson, secretary,
and treasurer be filled by three different people?
99)
100)
A manufacturer of widgets has three assembly lines: A, B, and C. The percentages of total
daily output that are produced by the lines are 25%, 35%, and 40%, respectively. The
percentages of defective units produced by the lines are estimated to be 1%, 2%, and 1%,
respectively. If a widget is randomly selected from a day’s production, what is the
probability that it is defective?
100)
101)
Two light bulbs are selected from a box of 20 bulbs. For this experiment, how many sample
points are in the sample space?
101)
102)
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?
102)
103)
Find the probability of rolling the same number in four throws of a fair die.
103)
104)
If P(E) = 0.2, P(F) = 0.6, and P(EF) = 0.12, determine if E and F are independent or
dependent.
104)
105)
If a fair red die and a fair green die are rolled, find the probability that the sum is greater
than 8, given that a 4 shows on the red die.
105)
106)
Determine 10P7
106)
107)
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?
107)
108)
Given the equiprobable sample space S=1, 2, ,3, 4, 5 and events E=1, 2, 4 and F=
1, 4, 5 , find P(E F).
108)
109)
Determine the value of 3P3·3C3 and simplify your answer.
109)
110)
If three cards are randomly drawn without replacement from a standard deck of 52 cards,
find the probability that all are queens.
110)
111)
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.
111)
112)
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?
112)
113)
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) E1= {the oldest and youngest work together doing the dishes; the middle child does
the dishes from a different meal}
(b) E2= {the youngest child has the day off}
(c) E3= {mom and dad do the dishes twice}
(d) E4= {the oldest child does the noon dishes alone}
(e) E‘2
(f) E3E4
(g) Let E5= {either the oldest or the youngest child does the morning dishes alone}
Let E6= {the middle child does the evening dishes alone}
E5E6
(h) E3E4
(i) E2E‘2
(j) E2E‘2
113)
114)
In a certain class, 40% of students had a B average at midterm. Of these, 50% ended up
with a course grade of B. Of those who did not have a B average at midterm, 40% ended up
with a course grade of B. If one of the students in the class is selected at random and is
found to have received a B for the course, what is the probability that the student did not
have a B average at midterm?
114)
115)
Determine the value of 4C2 and simplify your answer.
115)
116)
From a lot of ten computers, two are selected for extensive testing. In how many ways can
the selection be made?
116)
117)
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?
117)
118)
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?
118)
119)
In how many ways can a four–member committee be selected from a group of seven
people?
119)
120)
Determine 8C3
120)
121)
An urn contains three red and two green marbles, and a second urn contains two red and
two green marbles. An urn is selected at random and a marble is randomly drawn from it.
The marble is green. What is the probability that it came from the first urn?
121)
122)
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?
122)
123)
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.
123)
124)
If a die is rolled and then a coin is tossed, and the results are observed, determine the
sample space of this experiment.
124)
125)
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.
125)
126)
Determine the value of 5P1·5C3 and simplify your answer.
126)
127)
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?
127)
28
Answer Key
Testname: C8
29
Answer Key
Testname: C8
31
Answer Key
Testname: C8