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December 4th, 2010, 10:03 PM   #1
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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]
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December 5th, 2010, 04:37 PM   #2
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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.
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December 5th, 2010, 04:57 PM   #3
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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.
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December 6th, 2010, 01:17 PM   #4
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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
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