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CEE3770_Sum09_HW1_solns

# CEE3770_Sum09_HW1_solns - CEE 3770 Summer 2009 Homework...

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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

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(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.
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CEE3770_Sum09_HW1_solns - CEE 3770 Summer 2009 Homework...

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