Quiz-1-Fall-2005-06-Muna-Jurdak

# Quiz-1-Fall-2005-06-Muna-Jurdak - Time 1 hour Math 204 Date...

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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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Quiz-1-Fall-2005-06-Muna-Jurdak - Time 1 hour Math 204 Date...

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