HW3sol - IE 300 HW3 SOLUTIONS ASSIGNMENT: 2-187, 3-27, 33,...

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Unformatted text preview: IE 300 HW3 SOLUTIONS ASSIGNMENT: 2-187, 3-27, 33, 49, 66, 98, 114, 120, 136, 176 from the textbook 5 th edition. 2-187 (a) (30/50)*(29/49)*(28/48)=0.2071 (b) 30/48=0.625 (c) The probability can be written in terms of whether or not the first and second washer selected are thicker than the target. Let A1, A2 and A3 denote the events that the first, second and third washer selected are thicker than the target respectively. Thus P(A3)=P(A1A2A3 or A1A2A3 or A1A2A3 or A1A2A3) =P(A3|A1A2)P(A1A2)+ P(A3|A1A2)P(A1A2) + P(A3|A1A2)P(A1A2)+ P(A3|A1A2)P(A1A2) =P(A3|A1A2)P(A2|A1)P(A1)+ P(A3|A1A2)P(A2|A1)P(A1) + P(A3|A1A2)P(A2|A1)P(A1)+ P(A3|A1A2)P(A2|A1)P(A1) = gG G + gG G G + G G gG + G G gG =0.6 3-27 Let X denote the number of components that meet specifications; X = 0,1,2,3 P(X=0)=P(none of them meet specifications)=0.05*0.02*0.01=0.00001 P(X=1)=P(one of them meets specifications) =0.95*0.02*0.01+0.05*0.98*0.01+0.05*0.02*0.99=0.00167 P(X=2)=P(two of them meet specifications) =0.95*0.98*0.01+0.95*0.02*0.99+0.05*0.98*0.99=0.07663 P(X=3)=P(all of them meet specifications)=0.95*0.98*0.99=0.92169 3-33 From 3-15, we have P(X=-2)=1/8; P(X=-1)=2/8;...
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This note was uploaded on 01/26/2012 for the course IE IE 300 taught by Professor Zafarani during the Spring '09 term at University of Illinois, Urbana Champaign.

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HW3sol - IE 300 HW3 SOLUTIONS ASSIGNMENT: 2-187, 3-27, 33,...

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