 My Math Forum An engineering system consisting of n components
 User Name Remember Me? Password

 Advanced Statistics Advanced Probability and Statistics Math Forum

 December 4th, 2010, 10:03 PM #1 Newbie   Joined: May 2009 Posts: 25 Thanks: 0 An engineering system consisting of n components Problem: An engineering system consisting of n components is said to be a k-out-of-n system (k<= n)if and only if at least k of the n components function.Suppose all the components function independently of each other with a probability 1/2. Find the conditional probability that component 1 is working given that the system functions, when k=2 and n=3. Solution: Let A be component 1 functions i.e P(A) = 1/2 Let B be that 2 of 3 components function i.e P(B) = P(x=2;n=3;p=1/2) = 3*1/4*1/2 = 3/8 [using binomial probability] Therefore P(A/B) = P(A intersection B) / P(B) = P(A) * P(B) / P(B) = (1/2 * 3/ / (3/ = 1/2 [color=#FF0000][IS THIS SOLUTIONS CORRECT][/color] December 5th, 2010, 04:37 PM #2 Global Moderator   Joined: May 2007 Posts: 6,806 Thanks: 716 Re: An engineering system consisting of n components The definition says AT LEAST k out of n, so your calculation should also include the case where all 3 components are working. December 5th, 2010, 04:57 PM   #3
Newbie

Joined: May 2009

Posts: 25
Thanks: 0

Re: An engineering system consisting of n components

Quote:
 Originally Posted by mathman The definition says AT LEAST k out of n, so your calculation should also include the case where all 3 components are working.
Ok Thanks mate, and is it correct what i am doing. December 6th, 2010, 01:17 PM #4 Global Moderator   Joined: May 2007 Posts: 6,806 Thanks: 716 Re: An engineering system consisting of n components 2 cases: a) k=2 prob=3/8, prob 1 working = 2/3 b) k=3 prob=1/8, prob 1 working = 1 Therefore if system is working, Prob(1 is working)=(3/4)(2/3) + (1/4)1=3/4 Tags components, consisting, engineering, system Search tags for this page
,

# an engineering system consisting of n componenets said to be a k

Click on a term to search for related topics.
 Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post mac_alleb Linear Algebra 4 February 1st, 2014 06:57 PM kieroneng Linear Algebra 3 May 6th, 2013 12:31 PM wilhelm Applied Math 1 November 27th, 2012 03:27 AM ElMarsh Calculus 4 November 19th, 2009 07:44 PM shangwen_ren Number Theory 1 September 28th, 2009 10:59 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top

Copyright © 2019 My Math Forum. All rights reserved.      