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Math Help - An engineering system

  1. #1
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    An engineering system

    Question :
    An Engineering system consisting of n components is said to be k-out-of-n system (k \le n) if and only if atleast k of the n components function. Suppose that all components function independently of each other with the probability \frac{1}{2}. Find the conditional probability that component 1 is working given that the system funstions, when k=2 and n=3.
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  2. #2
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    One way to think about this

    If your 2 of 3 system is working, we must be in one of the following cases:

    BGG
    GBG
    GGB
    GGG

    where G=good (working machine), and B=bad. Isn't the probability that any particular machine is working then 3 of 4?
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  3. #3
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    Quote Originally Posted by qmech View Post
    If your 2 of 3 system is working, we must be in one of the following cases:

    BGG
    GBG
    GGB
    GGG

    where G=good (working machine), and B=bad. Isn't the probability that any particular machine is working then 3 of 4?

    here's what i could make of the question

    The component consist of n components and there probability is \frac{1}{2}

    ie.  P(x_i) = \frac{1}{2} .......where i = 0 ...n components


    is there any one who could help me with this question
    Last edited by mr fantastic; December 16th 2009 at 03:26 AM. Reason: Merged posts
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  4. #4
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    Quote Originally Posted by zorro View Post
    here's what i could make of the question

    The component consist of n components and there probability is \frac{1}{2}

    ie.  P(x_i) = \frac{1}{2} .......where i = 0 ...n components


    is there any one who could help me with this question
    Post #2 tells you how to do it (note that each of the outcomes is equally likely). Where are you stuck?
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    Is this correct?

    Quote Originally Posted by mr fantastic View Post
    Post #2 tells you how to do it (note that each of the outcomes is equally likely). Where are you stuck?

    Pr(Component functioning) = \frac{1}{2}

    Pr(2 out 3 components functioning)= Pr(B) = \frac{3}{5}

    Pr(1 st component functioning) = Pr(A)= \frac{1}{2}

    Pr(A|B) = \frac{Pr(A \cap B)}{Pr(B)} = \frac{Pr(A) . Pr(B)}{Pr(B)} = \frac{\frac{1}{2} . \frac{3}{5}}{\frac{3}{4}} = \frac{2}{5}

    Is this correct?
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  6. #6
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    Quote Originally Posted by zorro View Post
    [snip]
    Find the conditional probability that component 1 is working given that the system funstions, when k=2 and n=3.
    Do you mean
    Quote Originally Posted by zorro and edited by Mr F View Post
    [snip]
    Find the conditional probability that component 1 is working, given that the system funstions when k=2 and n=3.
    In other words, the system has three components and the given condition is that the system functions when k = 2 and n = 3? This is very different to what you posted.

    (Punctuation in the wrong place can completely change the meaning of something ....)
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  7. #7
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    Quote Originally Posted by mr fantastic View Post
    Do you mean

    In other words, the system has three components and the given condition is that the system functions when k = 2 and n = 3? This is very different to what you posted.

    (Punctuation in the wrong place can completely change the meaning of something ....)
    It is .............

    Find the conditional probability that component 1 is working given that the system functions, when k=2 and n=3.
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  8. #8
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    The question in the first post is correct

    Quote Originally Posted by mr fantastic View Post
    Do you mean

    In other words, the system has three components and the given condition is that the system functions when k = 2 and n = 3? This is very different to what you posted.

    (Punctuation in the wrong place can completely change the meaning of something ....)


    The question in the first post is correct, could u please tell me if the answer which i have posted above is correct or no , if not then why is it not correct
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  9. #9
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    Quote Originally Posted by zorro View Post
    The question in the first post is correct, could u please tell me if the answer which i have posted above is correct or no , if not then why is it not correct
    The wording in the first post is ambiguous to me so I can't say.
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  10. #10
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    Quote Originally Posted by mr fantastic View Post
    The wording in the first post is ambiguous to me so I can't say.
    Mr fantastic what should i do with this question ........I need to know whether the answer which i have posted is correct or no?
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