MAT 141
Chapter 7 Review
Spring 2012
1.
Name:
(4 pts) Use the given sets to define each of the following in roster form.
a. ACiB
|
b.
AVBUC
c.
cnfi
£
V =
i
I ..c.e.P,
I
\
or
^I { :/}
a
{&
c =
d. (AuB)nC
2.
b.
C
/ }
{c,d,g}
c'
{x\x 6
N and 3 < x < 12}
d.
£
< '
e
1 , 2 3> » - - ) 'I ^
?
;
J5 a letter in the word icosadodecahedron)
c. [x\x e l and x < 21}
f
c o^^,
J ) ^ ) ^>
x
n
^
r
^
'V I
2d
The set of months beginning with J.
(6 pts) For each of the following state whether it is true or false.
l~ ^SCc
a.
ZSFsl
c.
0 e {t, ft, 1,1,3,8}
e.
0 £ {t,fc,1,1,3,8}
WSC-p
i
4.
e
(4 pts) Express each of the following in roster form.
a.
3.
{a,b,c,d,e,f,g}
ru<L<
£
and B £ C, then
If A
d.
The set {1, 2, 3 , 2 0 } has 2
f.
The set of even numbers is a subset of the
integers.
A
£ C. T r w ^
b.
1 9
subsets.
^~
(2 pts) Some of the movies with all-time box office grosses include
Titanic($601 million)
Star Wars:Episode IV—A New Hope($461 million)
Shrek2 ($441 million)
E.T.the Extra-Terrestrial($435 million)
Star Wars:Episode I—The Phantom Menace($431 million)
Spider-Man($404 million)
The Lord of the Rings:The Return of the King($377 million).
Suppose that you have all seven films on DVD and decide, over the course of a week, to view some, all, or none
of these films. How many viewing options do you have?
5.
(4 pts) Use the chart to the right to answer each of the following.
a.
ADB
c.
6.
n(Al)B)
(3 pts) Answer each of the following as instructed.
a. Write the symbolic form of the shaded region.
u
.4""
/ 23
/ 29
\ 31
\37
/
\
\
53
59
61
67
71
If A: People with dental insurance, B: People
with eye insurance, and C: People with health
insurance, describe the shaded region in words.
11
C A ft' n 6'
or
7.
bi^t- net- d^/vfaL
(3 pts) Construct a Venn diagram illustrating the following sets: A={q, r, s, t, u}, B={q, r, s], C={r, u, w, yj, and
U={p, q, r, s, t, u, v, w, x, y}.
8.
(5 pts) A survey of businesspeople was taken to figure out where they purchased their coffee from. Of those
surveyed, 87 said Starbucks, 71 said Caribou, 80 made it at home, 62 made it at home and got it from Starbucks,
57 bought it from Starbucks and Caribou, 60 bought it from Caribou and made it at home, 50 did all three, and
12 said they do not drink coffee.
Fill in the Venn diagram below. Be sure to give me a legend to explain what your circles are.
Vote. I
fUt
9.
SurnJ&^tJ
&°
(6 pts) Use the hypothetical Venn diagram to answer the following,
a. How many respondents agreed with the statement? ^
B (African American)
b.
How many respondents disagreed with the statement?
c.
How many women agreed with the statement? ^
d.
How many people who are not African American agreed
with the statement?
Q
e.
How many women who are not African American disagreed
with the statement?
r>
f.
How many men who are not African American disagreed with the statement?
17-
A (Agree)
%
For problems 10-13 a die is rolled. Find the probability of
10. ( l p t ) Rolling a 6.
11. (1 pt) Rolling an odd.
y
\
12. (2 pts) Rolling an odd or a 2.
g
J_
t
_
fL
<e ~~
_
2/
3
45
jL-f.iL —. ~
13. (2 pts) Rolling an odd or greater than a 2.
Cc
Q>
0?
j—
- —
For problems 13-17 a card is drawn from a standard deck of 52. Find the probability of
14. (1 pt) Drawing a 7.
'
15. (1 pt) Drawing a face card (Jack, Queen, King).
16. (2 pts) Drawing a 3 or a face card.
M
\L
17-
^7 + ?L
%
a
17. (2 pts) Drawing a red card or a face card.
For problems 18-22 us the following chart.
Freshman
Men
50
Women
63
TOTAL
113
5^
Sophomore
44
51
95
<rz
<T2.
^2.
Junior
62
72
134
Senior
58
61
119
r
„CJ5"
TOTAL
214
247
461
18. (1 pt) What is the probability that a student chosen at random is a woman?
19. (1 pt) What is the probability that a student chosen at random is a junior?
20. (1 pt) What is the probability that a student chosen at random is a woman and a senior?
21. (1 pt) Given that a person chosen at random is a female, what is the probability that they are a Sophomore?
51
22. (1 pt)
Z17
P{Male\]unlor)
t
6,2
I3H
I3f
For problems 23-28 a bag of marbles has 4 reds, 5 blues, 4 black, and 3 green. Find the probability of
23. (2 pt) When choosing 3 marbles, withj^placement, that they are black, blue, black.
IG>
lb
\(o
'
°
n
&
24. (2 pts) When choosing 3 marbles, without replacement, that they are black, blue, black.
'cc
15^
25. (1 pt) When choosing 3 marbles, without replacement, that they are all green.
3
&
1
'
i S
1
' w
26. (1 pt) When choosing 3 marbles, without replacement, that none are green.
ic
IS"
'
H
27. (1 pt) What are the odds in favor of drawing a red?
1:n = IJJJ}
28. (1 pt) What are the odds against drawing a green?
t3 : 3
*<:.yv'j:-.';i.'U;.
;
For problems 29-30 the probability of a tornado hitting a certain town in any given year is 0.25.
29. (1 pt) What is the probability of a tornado hitting the town three years in a row?
30. (1 pt) What is the probability of no tornado hitting the town three years in a row?
(*-!>) (.15) (.75) = .H2I1
31. (3 pts) A study is taken where 85% of respondents were football fans, 22% of the respondents were hockey fans,
and 91% liked football or hockey. Fill in the appropriate amounts in the Venn diagram.
a. What percent liked football only?
b. What percent liked football and hockey?
c.
What percent liked neither?
V
9
/-
z z
~ -)Q,
32. (2 pts) At an insurance company 65% of companies' clients have home owners insurance and 30% own fire
insurance. It is also known that 20% have both. What is the probability that someone owns fire insurance, given
that they do not own homeowners insurance?
P(F|H') - P(FnH')
.0
33. (3 pts) Grade distribution broken down by major at a university.
Probability of an A
Department
B
i
'*
Portion of Students
enrolled in Department
Ki\\m)
.20 P(A|E )
.10 f ( f 1
.30 fi(f\\'
.02
Math
English
Science
Social Science
H
0.10
?(m)
0.25 p(t)
0.15
ftS)
o.30 90%)
0.20 p ( H )
History
.25 f ( f t l W )
If a person is chosen at random, what is the probability that they are a social science major, given they got an
A?
f ( S 5 | A)
1
s
r_7^S)t
M5€"
^-sX- >
3
^
J