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Math Help - Confused about multiplication rule.

  1. #1
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    Confused about multiplication rule.

    Here is the problem I have...

    A certain virus infects one in every 400 people. A test used to detect the virus in a person is positive 92% of the time if the person has the virus and 4% of the time if the person does not have the virus. (This 4% is called a false positive.) Let A be the event "the person is infected" and B be the event "the person tests positive." Find the probability, given a person tests positive, that the person really is infected.

    For some reason I cannot get the multiplication rule while everything else in stats has been a breeze. If someone could just tell me which numbers I use I'm sure I'll be good to go for awhile.
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  2. #2
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    What you really want to find is P(A|B) = \frac{{P(A \cap B)}}{{P(B)}}.

    You know that \begin{array}{rcl}<br />
   {P(B)} &  =  & {P(B \cap A) + P(B \cap A^c )}  \\<br />
   {} &  =  & {P(B|A)P(A) + P(B|A^c )P(A^c )}  \\ \end{array} .

    So P(A|B) = \frac{{P(B|A)P(A)}}{{P(B|A)P(A) + P(B|A^c )P(A^c )}}
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  3. #3
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    So it would be (1/400*.92)/.92?
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  4. #4
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    If I were you, I would think again.
    Why are you dividing by .92?
    What is P(B)?
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