MATH 204 Exam 2, Spring 2003
American University of Beirut · Mathematics for Social Sciences II · 5 pages
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LIBRARY
OF BEIRUT
QUIZ |: MATH 204 March 29 ,2003
6 7 8
For correctors only:
| Grade of Written Part Grade of Multiple Choice | Quiz | Grade
Number of Correct:......X 55.0000...
Total M.C. Grade=...0. oe
|
|
, Number of Wrong :......x(-1}
|
Instructions:
1 Write your name and I.D. and circle your section number.
2. The colored booklet is for scratch work and will not be corrected.
Answer table for the multiple choice questions. Write capital letters A, B,C, or D next to each question.
Part One(Written): Answer every part in the space provided for it ,and circle your final result .Do
not mention just the answer.
I. (10 points) Use Cramer’s rule to find x, if:
{ x,+x,+2,= 12
inom =3
3x, +x, -4x, = -6
-2. 6% /4-fR=
I. (20 points) Given the matrix: B -( aaa
2-7;
\ J
1. Use the gaussian procedure to find the inverse of the matrix B.
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LIBR AE ‘
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2. Use the result of part 1 above to solve the system:
~2x,+6x, =2
2x, - 7x, =-4
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OF BELRUT
Part Two: Answer the following 15 multiple choice questions on the answer sheet .You get:
5 points for each correct answer
-] for each wrong answer
Q for no answer
A box contains red, green, and blue balls .Some of the balls are striped and the others are dotted.
The following table gives the details.
| Red(R) Blue(B)
| Striped(S) 5 8
| Green(G) Total
14 1%
Dotted(D) = |7 | 6 0 en ac
| Total Laz 14 _4Y | So
One ball is randomly taken from the box. Answer questions 2, 3, 4, and 5.
2. Find P(B)
A. 8/17 B. 6/13 CH 715 D. 1/3
3. Find P(RUS)
A. 0.45 B. 0.8
4, Find P(D|B)
A. 2/3 B. 1/2 Cc. 5/14
5. The events R , S are :
A. Dependent B. Mutually exclusive B. Exhaustive D. Complementary
The probability that a student petition will be approved is 0.6. Three such petitions are
randomly selected .Answer questions 6 and 7.
6. What is the probability that all three will be approved?
A. 0.512 B. 0.180 C.0.216 D.0.242
7. What is the probability that only the first petition will be rejected?
A. 0.096 B. 0.340 C.0.240 D. 0.144
(S -1 3)
Given the matrix 4 = 2 1 4). Answer questions 8 and 9.
0 -2 1,
8. |4i=
A. 35 B. 62 C.-17
9. The cofactors of the second row are, respectively:
A. (-6 -7 10) B.@ -7 -1) C.¢5
0.7 0.35
|: Assume brands 1
ard
The transition matrix of a market dominated by two brands is 7 = ( )
and 2 currently each have 50% of the market share . Answer questions 10 and 11.
10. The market share of brand 1 in the next period will be:
A. 0.45 B. 0.35 C. 0.65 D. 0.25
11. What is the expected equilibrium share of brand 1?
A. 0.60 B. 0.30 Cc. 0.40 D. 0.25
A password consists of an English letter followed by three digits. Answer questions 12 and 13.
12. How many passwords are possible if there are no restricuions?
A. 10000 B. 52000 C. 18720 D, 26000
13. How many passwords are possible if the letter should belong to the word “prince”, and the digits
must be distinct and odd digits?
A. 144 B. 360 C.750 D, 1560
A box has 5 distinct statistics books, 4 distinct history books, and 3 distinct business books.
Answer questions 14 and 15.
14. Five books are selected at random from the box. If the books are not replaced in the box, what is
the probability of selecting a history book, a statistics book, two history books and a business book in
that order?
A BL D. =
264 420 99 1296
15. In how many ways can a student pick two books from the box if there are no restrictions?
A. 120 B. 66 C. 72 D. 10