Exam 1 - Version 1
This is a 50 minute test.
1. Of a group of 100 people, 33 like earrings, 29 like tattoos, and 26 like tattoos but don't like
earrings. How many like neither earrings nor tattoos?
(A) 59
(B) 41
(C) 38
(0) 12 (E) none of the others
2. In the diagram belovv,which of the following is true?
C.
I
(A) x E (A n G') U (B n G)
(0) x E (A n G) U (B' n G)
(B) x E (A U B) n (A' U G)
(E) none of the others
n G') n (B n G)
(C) x E (A
3. Two 6-sided dice are rolled. What is the probability that at least one of the dice shows a I?
(A) 1/3
(B) 1/12
(C) 11/36
(D) 1/6
(E) none of the others
4. A saleswoman is scheduling trips to visit 3 of the following 6 cities: Cleveland, Chicago, St.
Louis, Buffalo, Detroit, and Kansas City. A schedule is a list of the 3 cities in the order to be
visited. How many different schedules are there which include Kansas City?
(A) 60
(B) 120
(C) 20
(0) 24 (E) none of the others
,
5. Find n (A n B), given that A and B are subsets of U with
n (A) = 31, and n (B') = 10.
(A) 29
(B) 44
(C) 21
(D) 33
n (U) =
52,
n (A' n
B')
=
8,
(E) none of the others
6. A Greek urn contains a red ball, a blue ball, a yellow ball, and an orange ball. A ball is drawn
from the urn at random and then replaced. If one does this 4 times, what is the probability that
all 4 colors were selected?
(A) 1/70
(B) 3/32
(C) 2/9
(D) 1/4
(E) none of the others
7. A fortune teller foretells that each of 4 boys (Eric, Jason, Jeff, Kevin) will marry one of 4 girls
(Jodie, Lisa, Susan, Wendy). How many ways can this be done? (No divorces or bigamy please!)
(A) 12
(B) 6
(C) 44
(D) 24
7
(E) none of the others
Exam 1 - \ersi on 1
8. How many 4-letter words can be formed by rearranging the letters in the word "seek"?
(A) 12
(B) 24
(C) 6
(0) 24
(E) none ofthe others
9. Godzilla wants to destroy two buildings: a fast-food restaurant and either a tanning salon or a
public restroom. He sees the following buildings: 2 fast-food restaurants, 3 tanning salons, and
2.public restrooms. How many ways can Godzilla fulfill his desires?
(A) 10
(B) 21
(C) 12
(0) 7
(E) none of the others
10. I have 4 pencils, 3 ball-point pens, and a felt-tip marker in a cup on my desk. I choose a writing
implement from the cup randomly. What is the probability that it is not a ball-point pen?
(A) 1/3
11.
(B) 2/3
(C) 5/12
(D) 3/8
(E) none of the others
Captain Jean-Luc Picard has 3 blue shirts and 5 red shirts. He picked two at random to take on
a weekend trip to Earth. What is the probability that he took a shirt of each color?
(A) 1/15
(B) 2/7
(C) 8/15
(0) 15/28
(E) none of the others
12. Constance Noring has 5 cassettes by the Rolling Stones and 2 cassettes by R.E.M. She picks
three at random to listen to in her car. What is the probability that she takes 2 by the Rolling
Stones and 1 by R.E.M.?
(A) 2/35
(B) 2/7
(C) 13/35
(D) 4/7
(E) none of the others
13. Bob Smith watches the television talk shows on Wednesday morning. Mter each show he notes
whether it is dull, offensive, or good. He turns off the TV after seeing 1 dull shm.v,1 offensive
show, or if 3 shows have been watched altogether. How many outcomes are possible?
(A) 13
(B) 23
(C) 7
(0) 9
(E) none of the others
Numbers 14-16 are True/False
14.
n (A n B) + n (A
15. (A U B)'
U B)
= A' U B'
= n (A) + n (B)
for any sets A and B.
for any sets A and B.
16. Flip two coins and note the number of heads. The outcomes {O,1, 2} are equally likely.
13
}\-C ,4-11-
'Pi
1) A--A-E 1>]) c.
8
T t= 'f
Exam 1 - Version 2
This is a 75 minute test
1. Let A, B, and C be subsets ofa universal set U. Suppose n (A) = 12, n (B) = 16, n (A n B) =
7, n (A n C) = 9, n (B n C) = 11, n (A' n B' n C') = 7, n (A n B n C) = 5, and n (U) = 28.
Find n (C).
(A) 0
(B) 5
(C) 9
(D) 11
(E) 15
(F) none of the others
2. Licence plates in the state of Arkiana are constructed as follows: First there are two letters from
the set {A, B, C}, and then three distinct digits from the set {I, 2, 3, 4}. That is, letters may be
repeated, but digits may occur at most once. For instance, AA213 and CB432 are valid licence
plates, but AB112 is not valid. How many different licence plates can be produced?
(A) 24
(B) 33
(C) 144
(D) 216
(E) 576
(F) none of the others
3. An unfair coin is weighted such that "heads" come up four times as often as "tails".
probability should be assigned to the outcome "tails" to reflect this weighting?
(A) 3/4
(B) 1/4
(C) 1/5
(D) 4/5
(E) 1/3
What
(F) none of the others
4. How many 4 letter "words" can be formed from a set of 6 different letters if no letter can be
used more than once?
(A) 15
(B) 18
(C) 360
(D) 720
(E) 1188
(F) none of the others
5. Two fair dice are rolled, and the number shown by each die is recorded. What is the probability
that the difference between the numbers (i.e., number shown by the first die minus number shown
by the second die) is zero? Assume equally likely outcomes.
(A) 1/36
(B) 5/36
(C) 7/36
(D) 5/12
(E) 1/2
(F) none of the others
6. How many subsets with at least 2 elements does a set with 4 elements have?
(A) 2
(B) 6
(C) 10
(D) 11
(E) 12
(F) none of the others
7. A wallet contains two $1 bills and four $5 bills. Three bills are selected at random. What is the
probability that the total value of the selected bills is $11?
(A) 3/5
(B) 1/2
(C) 3/4
(D) 1/3
(E) 2/3
(F) none ofthe others
8. A student wants to take 2 classes this semester. She has 7 math classes and 5 biology classes to
choose from. In how many ways can she choose her classes if she can take either one math class
and one biology class, or two biology classes?
(A) 45
(B) 70
(C) 210
(D) 450
9
(E) 735
(F) none of the others
Exam 1 - \ersion 2
9. Let A and B be subsets of a universal set U. Which of the following statements is always true?
c
(A) (A U B)' = A' U B'
(C) A n B' c B n A'
(E) (A n B)' = Au B
(B) An B AU B
(0) (A n B)' = A' n B'
(F) none of the others
10. A committee contains 4 men and 3 women. Two members are selected at random to form a
subcommittee. What is the probability that both are women?
(A) 1/7
(B) 2/7
(C) 3/7
(0) 1/2
(E) 3/4
(F) none of the others
11. A box contains 2 red balls and 3 white balls. Two balls are selected at random, without replacement. Find the probability that at least one of them is white.
(A) 1/10
(B) 2/5
(C) 3/5
(0) 2/3
(E) 9/10
(F) none of the others
12. 5 women and 4 men compete in separate bike races. In both races, a gold medal is given to
the winner, and a silver medal to the runner-up. In how many different ways can the medals be
assigned?
(A) 16 (B) 20
(C) 32
(D) 60
(E) 240
(F) none of the others
13. In a group of 100 students interviewed about their preferred TV programs, 35 like Beavis &
Butthead, 55 like Saturday Night Live, and 30 dislike both of these shows. How many like both
shows?
(A) 10
(B) 20
(C) 35
(D) 45
(E) 70
(F) none of the others
14. Three boys playa game as follows. They put three white balls and a red ball in a box. Andy,
Bruce, and Charles, in this order, each choose a ball at random from the box, without replacement. Whoever gets the red ball wins. If none of the three draws the red ball, nobody wins.
Which one of the three boys has the largest probability of winning? Note: This problem may be
difficult - don t waste too much time on it if you cant solve it.
(A) Andy
(C) Charles
(E) not enough information given
(B) Bruce
(D) all three have the same probability
(F) none of the others
15. A hat contains 4 slips of paper numbered 1 through 4. An experiment consists of drawing two
slips of paper from the hat without replacement. Find the probability that the two numbers drawn
will add up to 5 or more.
(A) 1/4
(B) 1/3
(C) 1/2
(0) 2/3
(E) 3/4
(F) none of the others
16. A set X is partitioned into subsets X}, X2, and X3. The number of elements in Xl is twice the
number in X2, and the number of elements in X3 is six times the number in X2. Ifn (X) = 18,
10
••
••
Exam 1 - '\ersion 2
••
•
(A) 2
(B) 4
(C) 6
(0) 9
(E) 12
(F) none of the others
It
••
It
•
•
17. Suppose that 5 cards are drawn from a standard deck. In how many ways can it happen that
exactly three of them are spades?
(A) C (4, 3)
(0) C (4, 3) . C (48, 2)
(B) C (13, 3) . C (39, 2)
(E) C (13, 3) + C (39,2)
(C) C (13,3)
(F) none of the others
It
It
•
18. Suppose that A is the set ofIU students that live on campus, and B is the set ofIU students who
own a TV Which set describes those IU students who live off campus and own a TV?
•
(A) A' n B
(0) Au B'
•
•
(B) A n B'
(E) A' n B'
(C) A' U B
(F) none of the others
•
•
•
•
•
19. An experiment consists of first picking two names from a list of five names, then picking two
jobs from a list of four jobs, and finally picking two cities from a list of three cities. (Neither the
names nor the jobs or cities are ordered). How many outcomes are there for this experiment?
(A) 8
(B) 19
(C) 38
(0) 180
(E) 1440
(F) none of the others
•
•
~
I
l
I
20. A true/false test has 10 questions. Ron knows the answers to 7 of the questions, and he guesses
(probability of being correct = ~)on each of the other three questions. What is the probability
that he gets all 10 answers correct?
(A)
2~O
(B)
~g~:~~
(C)
l
(0) L~)3 (E)
11
1~
(F) none of the others
EXAM I - VERSION 1
1. A survey of 150 college students results in the following data:
102 read the student paper published by their school.
20 read the city paper.
85 who read the student paper but do not read the city paper.
How many of the students surveyed read the city paper but not the student paper?
a) 1
b) 2
c) 3
d) 4
e) none of the others.
2. A set X is partitioned into subsets Xl, X2 and X3• The number in Xl is twice the
number in X2 and the number in X3 is six times the number in X2• H n(X) = 18, find
neXt).
a) 2
b) 4
c) 6
d) 8
e) none of the others.
3. An experiment consists of drawing a ball from an urn which contains 2 red, 1 yellow, 1
white and 3 blue balls. After the color of the ball is noted, a second ball is drawn (with'}ut
replacement) and the color is noted. How many outcomes are in the event "both balls are
the same color?"
a) 0
b) 2
c) 4
d) 5
e) 8.
4. There are 6 black and 6 white mice available for an experiment which requires 4 mice.
H a random selection of 4 mice is made from the set of 12, what is the probability that 2
black and 2 white mice are selected?
a) 1/2
others.
b)
C(6,2),C(6,2)
C(12,4)
c)
C(6,2)+C(6,2)
C(l2,4)
10
d) 1/5
e) none of the
Exam I - Version 1
5. A shipper has 3 routes from New York to Chicago, 5 routes from Chicago to Denver,
and 6 routes from Denver to Los Angeles. In how many ways can merchandise be shipped
from New York to Los Angeles using these routes?
a) 14
b) 9
c) 90
d) 18
e) none of the others.
6. A hat contains 4 slips of paper numbered 1 through 4. An experiment consists of
drawing two slips of paper from the hat without replacement. Find the probability that
the two numbers drawn will add up to 4 or less.
show your work
7. A die is loaded so that some numbers are more likely than others. The number 1 is
twice as likely as the number 2 and the number 3 is three times as likely as the number 2.
Numbers 4,5,6 are all as likely as 2. What is the probability that a 1 will appear?
a) 1/9
. b) 2/9
c)
1/7
d) 2/7
e)1/3.
8. A subcommittee of 3 is selected from a committee of 3 men and 7 women. How many
-ways can the selection be made so that subcommittee contains both men and women.
show your work
11
Exam I - Version 1
9. An itinerary consists of three cities, visited in a certain order, from the choices New
York, Chicago, Denver, Los Angeles, and Thcson. How many itineraries are there that
include Chicago?
a) 60
b) 24
c) 36
d) 12
e) none of the others.
10. Suppose that 5 cards are drawn from a standard deck. How many ways are there for
exactly two of them to be spades?
a) C(4,2)
b) C(13,2)· C(39,3)
c) C(13,2)
d) C(4,2)· C(48,3)
e)none of the others.
11. Suppose that A is the set of employees that live in Bloomington and B is the set of
employees that drive their own car to work. Which set describes those employees that live
outside of Bloomington and drive their own car to work?
a) AnBe
e)none of the others.
b) AuB
12. Consider the following data concerning 160 students taking French, German, or RusSlan:
76 take French. 85 take German. 33 take French and German.
35 take German and Russian. 32 take French as their only foreign language.
15 take French, Russian, and German.
How many students take Russian? show your work
c
c
:3
12
EXAM I - VERSION 2
1. Let A, B, and C be subsets of a universal set U. Suppose n(A) = neB)
n(AnB) = 15, n(AnC) = 10, n(BnC) = 12, n(A'nB'nC')
= 20, n(AnBnC)
and n(U) = 80. Find n( C).
(a) 44
(b) 8
(c) 2
(d) 25
=
25,
= 3,
(e) none of the others
2. In a multi-step experiment, the first step is to roll a die and note the outcome (1,2,3,4,5,
or 6). Next, if the result on the die is even, then the die is rolled again, the result is
noted, and the experiment ends. If the result on the first die is odd, then a coin is
flipped twice, the number of heads is noted, and the experiment ends. Let S be the
sample space for this experiment. Find n(S).
(a) 36
(b) 24
(c) 27
(d) 30
(e) none of the others
3. Suppose each student in M118 is to be assigned a code number which starts with a
letter from the set {A, B, C, D, E, F} and then is followed by 3 digits each from the set
{1,2,3,4,5,6}.
For example, B-3-4-3 is one such code. How many such codes exist?
(a) 6 x P(7,3)
(c) 6
X
(d) 6 x C(7,3)
73
(e) none of the others
4. An unfair coin is weighted so that "heads" come up one third as often as "tails". What
probability should be assigned to the outcome "heads" to reflect this weighting?
(e) none of the others
5. An experiment consists of first picking two names from a list of six names, then picking
two jobs from a list of 5 jobs, and finally picking two cities from a list of 4 cities. How
many outcomes are there for this experiment?
(a) C(6,2) + C(5,2) + C(4,2)
(c) P(6,2)+P(5,2)+P(4,2)
(e) none of the others.
(b) 7200
(d) 900
6. How many 5 letter "words" can be formed from a set of 8 letters if no letter can be
used more than once?
(a) C(8,5)
(d) P(8,5)
(b) 1680
13
(e) none of the others
Exam I - Version 2
7. Two fair dice are rolled and the product of the two numbers is noted. What is the
probability that the product is less than 257
(a) ~
(b)
l~
(e) none of the others
(c) ~
8. How many subsets with 7 elements are in a set with 9 elements?
(a) P(7,5)
{c) 72
(b) P(7,2)
(d) 36
(e) none of the others
9. A purse contains 3 nickels and 5 dimes. Three coins are selected at random from the
purse. What is the probability that the value of the coins is 25 cents?
(a )
15
28
(b) ~
(d) ~
(c ) 13
28
(e) none of the others
10. A committee contains 5 men and 6 women. Two members are needed to fill the offices
of chair and vice-chair. How many ways can these offices be filled if both office holders
cannot be the same sex?
(a) 60
(b) P(6,2)+P(5,2)
(d) C(11,2) - G(6, 2) - G(5, 2)
(e)
(c) 120
none of the others
11. A psychology major is required to take 2 core biology courses and 2 core mathematics
courses. If there are 4 approved biology courses and 6 approved mathematics courses,
how many choices are available to satisfy these requirements?
(a) P(4,2)· P(6,2)
(d) C(6,2)· G(4,2)
(b) 45
(e) none of the others
(c) C(4, 2)
+ C(6, 2)
12. A true-false test has 10 questions. Sam knows the answers to 8 of the questions, and
he gue$$es (probability of being correct =
on each of the other two questions. '\That
is the probability that he gets all 10 answers correct?
!)
(a) ~
(b) C(lO,2)
P(10,2)
(e) none of the others
(c) -lr
13. An experiment, with equally likely outcomes, has a sample space S and an event E
with n(S) = 50 and PrIE] = .3. What is neE) ?
(a) 20
(b) 45
(d) 30
(c) 15
(e) none of the others
14. Two fair dice are rolled and the numbers on the two dice are noted.
proba.bility tha.t these numbers are different?
(a) ~~
(d) ~
14
What is the
(e) none of the others
Exam I - Version 2
15. An experiment has the sample space S = {O'}, 0'2,0'3}.
It is known that 0'1 and 0'2
occur equally often and 0'3 occurs three times as often as 0'1. What is W2 = Pr [{0'2 }]
?
(a) ~
(b)
t
(e) none of the others
(d) ~
(c) ~
16. Let U = {1,2,3, ... ,15} be a universal set with subsets E = {2,4,6,8},
F = {I, 3, 5,7, 9}, and G = {7, 8, 9, 10, 11, 12}. \\That is n«E U F)' n G')?
(a) 0
(b) 3
(d) 1
(c) 2
(e) none of the others
17. Let A and B be subsets of a universal set U. Which of the following is always true?
(a) An B' = A' n B
(c) (A U B)' = A' n B'
(e) none of the others
(b)A
nB =
(B
U
A)'
(d) (AUB)' =A'uB'
18. Which of the following is a true statement
about the point x in the Venn diagram to
the right?
(a)
(b)
(c)
(d)
(e)
x E An B
x E B UC
x E A' n B
x ~ B uC
none of the others
19. Let A and B be subsets of a universal set U. Suppose n(A
n(A' n B) = 10, and n(A U B) = 28. Find n(U).
(a) 18
(b) 38
(c) 48
(d) 18
n B) = 5, n(A' n B') = 10,
(e) none of the others
20. The 100 residents of Hickory, Indiana are asked if they like to watch basketball and/or
football. The results are that 87 like to watch basketball, 21 like to watch football,
and 8 tli&like both. How many like to watch both?
(a) 97
(b) 8
(d) 11
(c) 15
15
(e) none of the others
EXAM I - VERSION 3
1. (5 points) A and B are subsets ofa universal set U such that n(A) = 58, n(B) = 52, n«AUB)')
and n(U) = 177. Hov; many elements of U are in exactly one of the subsets A and B?
(A)
110
(F)
25
(B)
(G)
33
77
(C)
58
(B)
19
(0)
(J)
52
(E)
(K)
34
= lOa,
44
none of the others
2. (5 points) A cookie tray has 8 chocolat.e chip cookies, 11 "atmeal cookies, and 9 sugar cookies. If one
cookie is drawn at. random, what is the probability that it is a sugar cookie?
(A)
(F)
(L)
11/792
1/28
11/28
(B)
(G)
(C)
(B)
9/792
9/28
(0)
1/3
(E)
1/792
8/28
(J)
8/792
(K)
9/3,276
Done of the others
3. (5 points) A small furniture store has 4 sofas, 6 floor lamps, and 3 coffee tables on display. If Anne
buys one of each to furnish her living room, how many different outcomes of a sofa, a floor lamp, and a
coffee table are possible?
(A)
(F)
286
72
(L)
2,197
(B)
3
(G)
(M)
27
(B)
59,640
Done of the others
(C)
1,716
(0)
(J)
373,248
357,840
(E)
1
(K)
13
4. (5 points) Dan and Mary are taking their three children to the Nutcracker Ballet. They have tickets for
seats BIOI-I05. In how many different ways can the family sit in these seats if each person sits in one
of these seats and no one sits in someone's lap?
(A)
(F)
3,125
240
(B)
(G)
25
10
(C)
(B)
15
60
(0)
48
(J)
1
(E)
(K)
120
none of the others
5. (5 points) A shelf of books at the bookstore has 4 different detective novels, 5 different science fiction
books, and 4 different spy novels. If John selects 3 of these at random, how many different outcomes
are possible?
(A)
286
(F)
(L)
80
2,197
(B)
(G)
1,716
1
(M)
27
(C)
3
(0)
(B)
(N)
59,640
(J)
none of the others
72
13
(E)
(K)
357,840
373,248
6. (5 points) Joe, Anne, and Mike each select one of the 9 plays produced by the Theatre Department to
attend. If someone records who is going to which play, how man)' different outcomes are possible?
(A) 27
(F)
(K)
(B) 2,187
24
(G)
729
none of the others
(C)
(H)
504
9
16
(0)
84
(J)
19,683
(E)
512
Exam I - Version 3
7. (5 points) A survey of a group of 870 IU freshmen showed that 135 had attended a football game here,
110 had attended a women's basketball game here, 90 had attended a soccer game here, 35 had attended
a football game and a women's basketball game here, 25 had attended a football game and a socce~
game here, 15 had attended a women's basketball game and a soccer game here, and 10 had attended
all three types of games here. How many had attended none of these types of games here?
(A)
(F)
(K)
450
(B)
600
480
(G)
420
none of the others
(C)
510
(D)
(H)
520
(J)
360
270
(E)
500
8. (5 points) A group of investors has been classified according to whether they own stocks (S), bonds (E),
or mutual funds (M). The results are presented in the diagram below. How many own exactly one of
these three types of investments or do not own both stoeles and bonds.
(A)
235
253
175
150(E)
45
249
239
127
none
187
123
171
191
(M)
(B)
(H)
(J)of the others
(L)
(C)
(F)
(N)
(K)
(G)
(D)
9. (5 points) Dorm A has 5 single rooms (i.e., only one person per room) available and Dorm B has 6
single rooms available. If Sue, Ann, and Julie are each assigned one of these available rooms, how many
cii1ferent outcomes are possible?
(A)
165
(F)
(L)
990
3
(B)
(G)
4,060
30
(M)
90
(C)
(H)
(N)
1,331
(D)
24,360
(J)
none of the others
27
1
(E)
11
(K)
33
10. (5 points) A, B, and C are subsets ofa universal set U such that n(U) = 230, n(A) = 58, neB) = 35,
n( C) = 34, B n C = 0, and n «A U B U C)'} = 130. How many members of U are in exactly one of
the sets A, B. and C?
(A)
27
(B)
127
(C)
66
(F)
31
(G)
42
(H)
65
(L)
none of the others
(D)
(J)
130
230
(E)
(K)
73
insufficient information
11. (5 points) A cage contains 5 white mice, 7 grey mice, and 4 brown mice. If 3 brown mice and 2 gre;)'
mice are chosen at random for an experiment, how many different outcomes are possible?
(A)
(F)
84
(B)
2,520
(G)
(L)
113
(P)
1,008
4,368
(C)
232
25
(H)
none of the others
17
(D)
70
(E)
210
(J)
524,160
(K)
3,136
Exam I - Version 3
12. (5 points) Which of the following assignments of truth values make the sentence p V -
n
ill
none
of
the
others
None
p=Ft
q=Tt
1'=T
p=Ftq=Tt1'=F
nIIV
p=Ftq=FtT=F
p=Tt
and
only
and
only
nill
IV
q=Tt
only
only
onIy
only
1'=F
I,
I,
II,
onI)'
II,
ill,
and
and
III
IV
only
lit
and
IV
only
(D)
III
II
III
and
only
IV
IV
only
(I)
(E)
(P)
(Q)
TIt
ill,
and
IV
only
(M)
((H)
R)
(K)
(F)
It
ill,
and
IV
(G)
(C)
(L)
only
(q -+ 1') true?
(m)
(IV)
13. (5 points) A sandwich buffet has 6 different types of meat, 4 different types of cheese, and 5 different
types of bread. H Hank makes a sandwich using 2 types of meat, one type of cheese, and 1 type of
bread, how many different sandwiches could he make?
(A)
(F)
(K)
24
(E)
600
3,375
(G)
45
none of the others
14. (5 points) Is the sentence (AUB)'
false?
(A)
(D)
always true
(B)
none of the others
(C)
(H)
1,365
32,760
(D)
300
(J)
455
(E)
20
= A'uB' always true, always false, or sometimes true and sometimes
sometimes true and sometimes false
(C)
always false
15. (5 points) 6 assistants are to be assigned to administer exams in 3 different rooms: An 100, BH 120,
and CH 005. If 2 assistants are to be assigned to each room, in how many different ways can this be
done?
(A)
(F)
216
22
(B)
21
(G)
90
(C)
(H)
720
3,375
(D)
18
(J)
45
(E)
(K)
729
none of the others
16. (5 points) According to the rules of a game, if one lands in the dungeon, then to escape one must roll
a die until (i) the sum of the numbers rolled is at least 5 or (ii) some number has been rolled twice. If
one keeps a record of the numbers that are rolled as they are rolled, how many different ways are there
to escape from the dungeon.
(A)
(F)
51
44
(L)
(R)
(X)
60
45
47
(E)
58
(G)
(M)
52
57
(5)
71
(C)
(H)
(N)
(T)
(Y)
50
(Z)
70
30
62
41
none of
18
(D)
31
(J)
56
(P)
66
(U)
36
the others
(E)
(K)
(Q)
(V)
46
61
67
37
Exam I - Version 3
17. (5 points) A seminar class contains 7 seniors, 4 juniors, and 2 sophomores. If 4 of these students are
selected at random for a project, what is the probability that exactly 2 of them are juniors?
(A)
(F)
(B)
(G)
63/143
38/17,160
36/715
1/78
(C)
216/715
(E)
Done of the others
(D)
(E)
2/13
42/715
18. (5 points) The linen closet has 7 different white towels, 3 different brown towels, and 4 different yellow
towels. If Sam takes out 2 towels at random for his daughter to take to summer camp, what is the
probability that they are different colors?
(A)
84/182
(F)
84/91
(G)
Done of the others
(K)
(B)
30/91
61/182
(C)
14/91
(E)
77 /91
61/91
14/182
(D)
(J)
(E)
1/2
19. (5 points) A bucket of tennis balls contains 7 white balls, 3 yellow balls, and 2 orange balls. Joe takes
one ball at random from the bucket and serves it. Then he takes another ball at random from the bucket
and serves it. What is the probability that either the first ball is yellow and the second ball is white or
both balls are orange?
(A)
(E)
23/132
26/132
(B)
(F)
84/144
25/144
(C)
(G)
22/66
42/132
(D)
21/66
(E)
none of the others
20. (5 points) A sale table has 6 different white shirts. 4 different yellow shirts, and 3 different blue shirts.
If Anne buys 4 of these shirts for her husband, how many different possible outcomes have at least 1
blue shirt and at least 1 white shirt?
471
(B)
(F)
11,304
16,800
(C)
(G)
11,256
126·,
469
(K)
1,980
(L)
none of the others
(A)
990
(E)
(J)
19
(D)
(E)
700
111