_MACM-2023-02-03-SampleTest1
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Simon Fraser University *
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Course
201
Subject
Mathematics
Date
Feb 20, 2024
Type
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************ Samples midterm test ***************
MACM 201 D400, Spring 2023
Midterm Test 1
February 3, 2023, 8:30 – 9:20
SFU Email:
@SFU.CA
Signature:
First Name:
Last Name:
SFU ID #:
Question:
1
2
3
4
5
Total
Points:
10
10
10
10
10
50
1. Do not open this booklet until told to do so.
2. Write your name, SFU student number and email ID in the space provided.
3. Write your answer in the space provided. If additional space is needed use the back of the previous
page.
4. To receive full credit for written questions, your solution must include justification or detailed calcula-
tions, is complete and well presented.
5. Simple Scientific calculators, without combinatorial calculation capabilities, may be used. No other
aids such as books, papers, or electronic devices allowed.
6.
During the examination, copying from, communicating with, or deliberately exposing writ-
ten papers to the view of, other examinees is forbidden.
************ Samples midterm test ***************
MACM 201 D400, Spring 2023
Midterm Test 1
Blank page for extra work
************ Samples midterm test ***************
MACM 201 D400, Spring 2023
Midterm Test 1
1.
[10]
Choose the correct answer. Select only one answer
(a) How many ways 6 jobs can be assigned to 6 machines in such a way that no machine can take more
than one job and all jobs must be completed?
36
ways
720
ways
12
ways
(
6
6
)
ways.
(b) The number of 5 digit numbers that can be formed using the digits
0
,
1
,
2
,
3
,
4
so that no digit is
repeated is
96
.
120
.
216
.
none of the above answers are correct.
(c) How many circular arrangements are possible for the letters A,B,C,D,E,F,G, if A and B are required
to be non-adjacent
720
.
240
.
480
.
correct answer is not given.
(d) The coefficient of
x
4
y
5
in the expansion of
(4
x
-
5
y
)
9
is
-
201
,
700
,
000
201
,
700
,
000
201
,
600
,
000
.
-
201
,
600
,
000
(e) A drawer contains 12 pairs of different socks and a person is drawing one by one to find a matching
pair. What is the maximum number of draws required to obtain a matching pair
12
23
24
13
************ Samples midterm test ***************
MACM 201 D400, Spring 2023
Midterm Test 1
Blank page for extra work
************ Samples midterm test ***************
MACM 201 D400, Spring 2023
Midterm Test 1
2.
[10]
Choose the correct answer. If more than one answers are correct, choose all of them.
(a) Choose the correct statements.
If
A
1
, A
2
, . . . , A
n
are
n
mutually independent events, then,
P
(
A
1
∩
A
2
∩
. . .
∩
A
n
) =
P
(
A
1
) +
P
(
A
2
) +
· · ·
+
P
(
A
n
)
If
X
1
and
X
2
are two random variables defined over the sample space
S
, then
E
(
X
1
+
X
2
) =
E
(
X
1
) +
E
(
X
2
)
and
E
(
αX
1
) =
αE
(
X
1
)
, where
α
is a real number.
The probability of a given pattern of
k
successes and
n
-
k
failures out of
n
independent
Bernoulli trials is
(
k
n
)
p
k
q
n
-
k
.
If
A
and
B
are any two events from a sample space then
P
(
A
∩
B
)
≤
P
(
A
) +
P
(
B
)
-
1
.
(b) The convolution of the sequences
h
1
,
1
,
1
,
1
. . .
i
and
h
1
,
-
1
,
1
,
-
1
. . .
i
is
h
0
,
1
,
0
,
1
,
0
. . .
i
h
2
,
0
,
2
,
0
,
2
,
0
. . .
i
h
0
,
2
,
0
,
2
,
0
. . .
i
h
1
,
0
,
1
,
0
,
1
,
0
. . .
i
(c) Choose the correct statement
The OGF
(1 +
x
)
n
generates
(
n
0
)
,
(
n
1
)
,
(
n
2
)
, . . . ,
(
n
n
)
,
0
,
0
, . . .
The EGF
(1 +
x
)
n
generates
P
(
n,
0)
, P
(
n,
1)
, P
(
n,
1)
, . . . , P
(
n, n
)
,
0
,
0
,
. . . .
The OGF
1
1
-
x
generates
h
1
,
0
,
1
,
0
. . .
i
The EGF
1
1
-
x
generates
h
1!
,
0
,
3!
,
0
,
5!
. . .
i
(d) Find the correct statements
For any positive integer
n
,
P
(
n,
4) = 42
P
(
n,
2)
P
(
n, r
) =
nP
(
n
-
1
, r
)
(
n
r
)
=
(
n
k
)
if
r
=
k
or
r
+
k
=
n
.
The value
(
0
0
)
is indeterminate
(e) A committee of six people needs to be formed out of 15 people of which 7 are men and 8 are women.
What is the probability that the committee is gender balanced (same number of men and women).
(
7
3
)
(
15
6
)
(
7
3
)(
8
3
)
(
15
6
)
(
8
3
)
(
15
6
)
The correct answer is not given.
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