This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: IEOR 172: Probability and Risk Analysis for Engineers, Fall 2007 Homework 2 Solution Chapter 3 Question 9 Denote A as urn A, and W as white ball: P( A = 2 W  2 W ) = P( A = 2 W, 2 W ) P(2 W ) = 2 6 8 12 3 4 + 4 12 1 4 2 6 8 12 3 4 + 2 6 4 12 1 4 + 4 6 8 12 1 4 = 7 11 Question 12 Denote F as fail the exam, F i as fail the i th exam: (a) P( F c ) = 0 . 9 . 8 . 7 = 0 . 504. (b) P( F 2  F ) = P( F  F 2 )P( F 2 ) P( F ) = 1 . 9 . 2 1 . 504 = 0 . 3629 . Question 25 Let p denote the proportion of people in this town who are over 50. Let 1 denote the proportion of time that a person under the age of to spends in the streets, and 2 be the corresponding value for those over 50. Denote S as people on the street, then this method only compute the conditional probability of people over 50, P(over 50  S ) = P(over 50 ,S ) P( S ) = 2 p 1 (1 p ) + 2 p . When 1 2 , this value is approximately equal to p . Question 37 Denote H as head, T as tail, F as fair coin and uF as unfair coin: (a) P( F  H ) = P( H  F )P( F ) P( H  F )P( H ) + P( H  uF )P( uF ) = 1 2 1 2 1 2...
View
Full
Document
 Fall '07
 righter

Click to edit the document details