MTH U115 Sample Midterm Exam Questions — Spring 2008
Let
U
=
{-
1
,
0
,
1
,
2
,
3
,a,b,c,d
}
,
R
=
{
2
,
3
,b,c
}
,
S
=
{-
1
,
0
,c,d
}
,
and
T
=
{
0
,
2
,a,c
}
Use this information to answer questions #1 and #2.
1. Find (
R
0
∩
T
)
A)
{
0
,a
}
B)
{-
1
,
0
,
1
,a,c,d
}
C)
{
0
,
1
,a
}
D)
{
2
,c
}
E) None
Answer # 1:
2. Find (
S
∪
T
)
0
A)
{-
1
,
1
,
2
,
3
,a,b,d
}
B)
{
3
}
C)
{-
1
,
0
,
1
,
2
,a,c,d
}
D)
{
0
,c
}
E) None
Answer # 2:
3. A pair of fair dice (one red, one green) are rolled. What is the probability that the
sum rolled is a 2, 3, or 12 (“craps”)?
A)
1
9
B)
1
4
C)
1
12
D)
1
3
E) None
Answer # 3:
4. A pair of fair dice (one red, one green) are rolled. What is the probability that the
ﬁrst die shows a 4 or the sum rolled is a 6?
A)
5
18
B)
11
36
C)
1
6
D)
2
9
E) None
Answer # 4:
5. A candy manufacturer makes 7 kinds of dark chocolate candies and 5 kinds of white
chocolate candies. A sample package contains 3 kinds of dark chocolate and 2 kinds
of white chocolate candies. How many diﬀerent sample packages can be prepared?
A) 350
B) 35
C) 45
D) 4,200
E) None
Answer # 5:
6. The program committee for a folk music festival must arrange 7 numbers for an
evening performance. There are 12 numbers available. How many diﬀerent ar-
rangements of the evening performance are possible?
A) 95,040
B) 792
C) 5,040
D) 3,991,680
E) None
Answer # 6:
7. A group of 4 students is to be selected from a group of 10 students to take part in
a class in cell biology. In how many ways can this group be chosen?
A) 5,040
B) 240
C) 210
D) 40
E) None
Answer # 7:
8. How many diﬀerent 5-letter words beginning with two vowels can be formed from
the letters in the word PECULATOR, if repetition is not allowed and there are no
other restrictions?
A) 720
B) 2,520
C) 4,032
D) 126
E) None
Answer # 8:
The Business Students Club is composed of 20% sophomores, 35% juniors, and
45% seniors. The Accounting Department was interested to learn that 15% of the
sophomores are accounting majors, as are 10% of the juniors and 21% of the seniors.
Use this information to answer questions #9 and #10.