# 2006%20fall - Math 218 Final Examination Fall 2006...

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Math 218 Final Examination: Fall 2006 Name (Printed) Student ID Signature (handwritten) Directions. Fill out your name, signature, and student ID number on the lines above; then checkmark the lecture time and discussion time in the space provided below. Do not OPEN the test booklet until instructed to do so. After you are so instructed, make sure all 11 pages are present (not including tables, which are distributed separately). Note that the separately distributed sheet of tables is printed on both sides. On this examination, you may use a calculator and one 8-1/2 by 11-inch sheet of handwritten notes (both sides may be written on). No books or other notes are permitted. When an answer box is provided, copy your answer into that box. Numerical answers should be evaluated to be either decimals or fractions. Numerical answers alone are not suﬃcient; you MUST indicate how you derived them (show your work). When submitting a numerical answer which is a decimal, give three accurate digits following the decimal point; when submitting a fraction, make sure it's reduced to lowest terms. Be sure to include the appropriate units (for example, feet, pounds, mph, etc.). All problems are equally weighted ( 10 problems at 20 points each = 200 points total). Check one lecture time: 9:00 MWF (Bruck) 10:00 MWF (Bruck) 10:00 MWF (Mesyan) 11:00 MWF (Lin) 11:00 MWF (Verona) 12:00 MWF (Mesyan) 12:00 MWF (Lin) 1:00 MWF (Verona) 2:00 MW (Mesyan) 2:00 MW (Lin) Check one TTh discussion time: 8:00 9:00 10:00 11:00 12:00 1:00 2:00 3:00 4:00 Do not write on this page below this line! 1 (20 pts) 6 (20 pts) 2 (20 pts) 7 (20 pts) 3 (20 pts) 8 (20 pts) 4 (20 pts) 9 (20 pts) 5 (20 pts) 10 (20 pts) (100 pts) (100 pts) Total Points 1

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2 Problem 1 (20 pts) . 30 marbles are sitting on a table: 6 red, 9 blue, and 15 green. All of the red marbles, 3 of the blue marbles, and 10 of the green marbles are covered in chocolate, because a child played with them while eating a piece of pie. The remaining marbles were out of the child's reach and remained clean. (a) Draw a probability tree describing the situation. Be sure to include the labels of events, probabilities, and conditional probabilities. (b) If a randomly selected marble is covered in chocolate, what is the probability that it is red?
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