1. ## 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.

2. What you really want to find is $\displaystyle P(A|B) = \frac{{P(A \cap B)}}{{P(B)}}$.

You know that $\displaystyle \begin{array}{rcl} {P(B)} & = & {P(B \cap A) + P(B \cap A^c )} \\ {} & = & {P(B|A)P(A) + P(B|A^c )P(A^c )} \\ \end{array}$.

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

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

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