MATH 210
Final Exam
May 2, 1996
1.
Consider the matrix T below.
Which of the following is true?
(a)
T is absorbing stochastic and has 6 absorbing states.
(b)
T is absorbing stochastic and has 2 absorbing states.
(c)
T is not absorbing stochastic but has 6 absorbing states.
(d)
T is not absorbing stochastic and but has 2 absorbing states.
(e)
None of the above.
2.
Mom and Dad and their 3 children line up for a picture. How many different pictures can be taken if Mom will not stand next to Dad ?(a)
72
(b)
48
(c)
80
(d)
64
(e)
None of the above.
For the next three problems consider the following:
In a class of four, grades on a ten point quiz are: 8,5,3,8.
3.
The mean grade is:(a)
24
(b)
7
(c)
6
(d)
4
(e)
None of the above.
4.
The variance of the grades is:(a)
(b)
11/2
(c)
9/2
(d)
(e)
None of the above.
5.
The standard deviation of the grades is:(a)
(b)
11/2
(c)
9/2
(d)
(e)
None of the above.
6.
I play the following game with each of the 1000 Math students:Toss an unbiased die twice.
If the top number is even both times the student wins $50.
If the top number is odd both times the student gives me $10.
Otherwise, the student gives me $25.
Approximately, how much money am I likely to win/lose?
(a)
I win $1,000
(b)
I win $2,500
(c)
I lose $2,500
(d)
I lose $1,000
(e)
None of the above.
7.
A radio contains 12 electronic components of which 3 are defective. If four are selected at random, what is the probability that at least one is defective?(a)
14/55
(b)
41/55
(c)
1/3
(d)
1/4
(e)
None of the above.
8.
If Pr(E)=1/7,
and E, F are independent events, then Pr(F)=
(a)
1/8
(b)
3/28
(c)
1/28
(d)
4/7
(e)
None of the above.
9.
If Pr(E)=1/7,
and E, F are mutually exclusive events, then Pr(F)=
(a)
1/8
(b)
3/28
(c)
1/28
(d)
4/7
(e)
None of the above.
For the next two problems, refer to the following situation.
A certain car, the Deathtrap, is manufactured at four plants A, B, C, D which produce .3, .2, .4, and .1 of the cars, respectively. Of the cars made at plant A, B, C, D the percentages with a major defect are 5%, 5%, 10% and 15%, respectively.
10.
What is the probability that a Deathtrap is defective?(a)
0.06
(b)
0.08
(c)
0.10
(d)
0.12
(e)
None of the above.
11.
Suppose a Deathtrap is defective. What is the probability that it came from plant A?(a)
3/5
(b)
3/8
(c)
3/16
(d)
2/5
(e)
None of the above.
For the next two problems maximize M = 15x + 5y subject to:
12.
The maximum of M is:(a)
10
(b)
6
(c)
90
(d)
5
(e)
None of the above.
13.
The maximum occurs when x =(a)
2
(b)
12/5
(c)
11/5
(d)
9/5
(e)
None of the above.
14.
If Pr(E) = 0.4, Pr(F) = 0.6 and
then Pr(F|E)=
(a)
0.75
(b)
0.5
(c)
0.18
(d)
0.24
(e)
None of the above.
15.
Consider the system:x + 2y + 3z + 5w = 1
x + 3y + 8z + 4w = 3
2x + 5y + 12z + 25w = 5
4x + 10y + 23z + 35w = 7
Given:
In the solution:
(a)
w = 0
(b)
w = 1
(c)
w = -1
(d)
w = -2
(e)
None of the above.
16.
The slope of the line 91x - 51y = 4357 is:(a)
51
(b)
91
(c)
51/91
(d)
-51/91
(e)
None of the above.
17.
Compute C(10,000,9998)(a)
2000
(b)
99,990,000
(c)
100,000,000
(d)
2
(e)
None of the above.
18.
Consider the following survey results:1000 students are surveyed about which meals they ate in their dormitory cafeteria:
250 ate breakfast and lunch,
350 ate breakfast and dinner,
500 ate lunch and dinner,
200 ate dinner ONLY,
400 ate breakfast,
600 ate lunch,
350 ate dinner and not lunch.
How many ate exactly two meals in their dormitory cafeteria?
(a)
250
(b)
300
(c)
400
(d)
550
(e)
None of the above.
19.
Solve the system:x - y + 3z = 4
y - 3z = -7
y + 3z = 33
(a)
In the solution: y = 1
(b)
In the solution: y=13
(c)
There are infinitely many solutions.
(d)
No solutions; the equations are inconsistent.
(e)
None of the above.
20.
If possible find the inverse of
(a)
The entry in the first row and the first column of the inverse is: 1
(b)
The entry in the first row and the first column of the inverse is: 2
(c)
The entry in the first row and the first column of the inverse is: 3
(d)
The matrix is not invertible.
(e)
None of the above.
21.
Which of the following matrices are invertible?
(a)
All except C.
(b)
A and D only.
(c)
A and B only.
(d)
A only.
(e)
Some other selection.
For the next two problems consider the following:
A simple economy has 2 industries: oil and gas. The production of $1 of oil requires $0.20 in oil and $0.10 cents in gas, while the production of $1 of gas requires $0.40 cents of oil and $0.80 cents of gas. Assume there is an external demand for $240 of oil and $480 of gas.
22.
How much oil should be produced to satisfy demand?(a)
$2,000
(b)
$3,000
(c)
$3,400
(d)
$4,200
(e)
None of the above.
23.
How much gas should be produced to satisfy demand?(a)
$2,000
(b)
$3,000
(c)
$3,400
(d)
$4,200
(e)
None of the above.
24.
Which of the following lines passes through the point ( 2, -1) ?(a)
7x + 2y = 16
(b)
7x - 2y = -16
(c)
-7x + 2y = -16
(d)
7x + 2y = - 14
(e)
None of the above.
25.
Find the top right entry of the stable matrix for:
(a)
0
(b)
1
(c)
0.1
(d)
0.3
(e)
None of the above.
26.
Which of the following are regular stochastic matrices?
(a)
A only.
(b)
A and B only.
(c)
B and C only.
(d)
A and C only.
(e)
Some other selection.
For the next three problems, consider the following information.
A group attempting to fight cancer in a large city began an active campaign against smoking. For each of several months a survey was conducted. On the basis of their study, they found they could predict that 80% of adults who smoke in any given month will continue to do so in the next month while 5% of adults who do not smoke in any given month will smoke the next month.
27.
If initially 30% of the adult population smoked, what percentage will still be smoking next month?(a)
25%
(b)
30%
(c)
32.5%
(d)
22.5%
(e)
None of the above.
28.
If the campaign is continued over a long period of time, approximately what fraction of the adult population will continue smoking?(a)
1/4
(b)
1/5
(c)
1/6
(d)
1/7
(e)
None of the above.
29.
In a group of 100 students, 40 take English, 50 take Math, and 20 take exactly one of these subjects. If a student is selected at random, what is the probability that they take neither English nor Math?(a)
7/10
(b)
9/20
(c)
1/10
(d)
7/20
(e)
None of the above.
30.
An unbiased coin is tossed 3 times and the sequence of heads and tails observed. Are the events "Get an even number of heads" and "Get more heads than tails" independent?(a)
Yes
(b)
No
(c)
0.3
(d)
0.7
(e)
None of the above.
© Department of Mathematical Sciences, Northern Illinois University, DeKalb IL 60115
Prepared 11/27/97 by Dr. Anders Linnér (
alinner@math.niu.edu)