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Unformatted text preview: Time: 1 hour Math 204 Date: October
Quiz 1
First Semester 05/06
Instructor: Mrs. Muna Jurdak Section 9 Tues. 3:30 Section 10 Tues. 2:00 Section 11 Tues. 12:30 Section 12 Tues. 11:00. Instructions:
1. Write your name and ID number clearly where indicated.
2. Circle your section number above, according to the time of the problem
solving session in which you are enrolled. 3 Solve the problems on this, the white question sheet. Use the colored sheets
for scratch work only. You may use the back of a white sheet to complete the solution of a problem. Problem I 1'10
Problem 2 /20
Problem 3 / 10
Problem 4 f15
Problem 5 I10 Problem 6 [20 Problem 7 /15 Total /100 i (10%) 1. Given the matrices, 1 6 1
—1 4 2 1 A= ,B'= , C= 0 2 , D= 0
1 5 3 1 3 1 0 Perform the following operations, if possible.
(a) A+2B (b) AC (c) CB ((1) CTD. 0 0
1 0 .
O 1 20%) 2. (a) Using the cofactor method, ﬁnd the inverseidfﬂie matrix A, 4
A=2
1 (b) Write the following system of equations in matrix form. Then solve the
system using matrices. 4x}. + X2 +2X3 = 0
2X] +5X2 = x1+2x2 +3X3= 4 (10%) 3.Using the Gaussian procedure, ﬁnd the inverse of the following matrix
A, if the inverse exists. (3 If) (15%) 4. A game consists of ﬂipping a coin followed by rolling a die. Let A = the event of getting a head and then an even number on the die.
B = the event of getting a head and then an odd number on the die.
C = the event of getting a tail and then a number 4 or more on the die.
D = the event of getting a tail and then a number 5 or less on the die. (21) Find the following probabilities:
p(A')a p(C), PUD), and MC U13)
(b) Are the events A, B, C, D (i) Mutuaily exclusive?
(ii) Collectively exhaustive? Give reasons for your answers for part (b). (10%) 5. A box contains 7 red marbles and 4 white marbles. Three marbles are
drawn from the box one after the other (without replacement). Find the
probability that the ﬁrst 2 are red and the third is white. (20%) 6. Seven squares, 4 red, 3 green, are to be arranged in a row. Find the
number ofways that this can be done: (a) if there are no restrictions
03) if squares of the same color must be next to each other. (e) If the green squares only must be next to each other. (15%)7. (a) A woman has 12 close friends. Find the number of ways that she can invite 5 of them to dinner.
(b) If two of the woman's friends are married and will not attend separately, ﬁnd the number of ways that the woman can invite 5 of her
12 friends. ...
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 Three '10
 RomyArbid
 Math

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