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Unformatted text preview: CEE 3770  Summer 2009 Homework 1 (due on 05/21) 1. (6 points) Let E,F,G be three events. Suppose that U = E F G . Find expressions for the events that of E,F,G (a) only F occurs. Solution: E F G (= E G,sinceU = E F G ) (b) both E and F occur, but not G. Solution: E F G (c) at least one event occurs. Solution: E F G (= U ) (d) at least two events occur. Solution: ( E F ) ( E G ) ( F G ) (e) all three events occur. Solution: E F G (f) none occur. Solution: E F G (= ), since none is the opposite of at least one 2. (6 points) A box contains 3 marbles (two red and one blue). Consider an experiment that consists of taking one marble from the box, then replacing it in the box, and then drawing a second marble from the box. (a) What is the sample space? Solution: S = { RR,RB,BR,BB } (b) Is it SSS(Simple Sample Space)? If not, construct a simple sample space. Solution: No. Clearly BB occurs with smaller probability (=1/9). A simple sample space, S = { R 1 R 1 ,R 1 R 2 ,R 1 B,R 2 R 1 ,R 2 R 2 ,R 2 B,BR 1 ,BR 2 ,BB } (c) Find the probability that at least one blue marble is chosen. Solution: From S , 5 9 . 3. (6 points) Repeat the above when the second marble is drawn without replacing the first marble. (a) What is the sample space? Solution: S = { RB,RR,BR } (b) Is it SSS(Simple Sample Space)? If not, construct a simple sample space. Solution: Yes. Pr ( RB ) = 2 3 1 2 = 1 3 Pr ( RR ) = 2 3 1 2 = 1 3 Pr ( BR ) = 1 3 1 = 1 3 1 (c) Find the probability that at least one blue marble is chosen. Solution: Since S is SSS, 2 / 3 4. (6 points) On a surprise quiz with two questions, the first question is multiple choice with a,b,c and d (4 alternatives) while the second question is a true/false question. A student is completely unprepared for the quiz and answers at random. (a) Give a sample space for this experiment. Solution: S = { aT,aF,bT,bF,cT,cF,dT,dF } (b) The instructor is interested in the number of points on this quiz. Correct answer on the first question carries 5 points and incorrect 1 point. Correct answer on the second question carries 5 points, incorrect 3. Give a sample space for this experiment andquestion carries 5 points, incorrect 3....
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This note was uploaded on 06/29/2009 for the course CEE 3770 taught by Professor Staff during the Spring '08 term at Georgia Institute of Technology.
 Spring '08
 Staff

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