CEE3770_Sum09_HW1_solns - CEE 3770 - Summer 2009 Homework 1...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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....
View Full Document

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.

Page1 / 6

CEE3770_Sum09_HW1_solns - CEE 3770 - Summer 2009 Homework 1...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online