Confused about multiplication rule.

**StonedApe** · October 7th 2008, 01:38 PM

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.

**Plato** · October 7th 2008, 01:57 PM

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 $P(A|B) = \frac{{P(B|A)P(A)}}{{P(B|A)P(A) + P(B|A^c )P(A^c )}}$

**StonedApe** · October 7th 2008, 02:15 PM

So it would be (1/400*.92)/.92?

**Plato** · October 7th 2008, 03:14 PM

If I were you, I would think again.
Why are you dividing by .92?
What is P(B)?

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