This preview shows page 1. Sign up to view the full content.
Unformatted text preview: Section 7.4 197 28. We use induction on n, the strong form. If n = 2, the right hand side of the equation is just P(A1)P(A2 1 AI) = P(A1) P~(A~:1 = P(A2 n AI), which is the left hand side, so the state ment is true. Now assume n > 2 and the result holds for all k, 1 :::; k < n. We have P(A1 n A2 n ... nAn) = P((A1 n A2 n nAnI) nAn) = P(A1 n A2 n ... n AnI)P(An I Al n A2 n ... n AnI) by the k = 2 case = [P(A1)P(A2 1 AI) ... P(An 1 I Al n A2 n ... n An 2)] P(An I Al n A2 n ... nAnI) by the k = n  1 case, and this is the right hand side. By the Principle of Mathematical Induction, the result follows. 29. [BB] Let A, B, C be the events of eating at Leonce's, Harold's, and Vegan Delights, respectively, and let D be the event a customer is satisfied. We are given that P(A) = .4, P(B) = .35, P(C) = .25, P(D I A) = .85, P(D I B) = .9, P(D I C) = .95. (a) P(D n C) = P(C)P(D I C) = .25(.95) = .2375....
View Full
Document
 Summer '10
 any
 Graph Theory

Click to edit the document details