#### RiskNoob

##### Active Member

I think the question regarding Bayes' theorem was something like this:

Given

P (positive | fraud ) = 1

P (negative | not fraud) = 0.95 (hence P (positive | not fraud) = 0.05)

P ( fraud ) = 0.001

What is P (fraud | positive) ?

P (fraud | positive) = P(fraud) / P(positive) * P(positive | fraud) , by Bayes’ Theorem

= P (fraud) / [ P(positive | fraud)*P(fraud) + P(positive | not fraud)*P(not fraud) ] * P(positive | fraud)

Plug in the numbers to find the answer