# Discrete Prob

• May 3rd 2011, 10:06 AM
dwsmith
Discrete Prob
This question was on my first probability test and I got the first part wrong. Therefore, could someone show me how to do it?

One half percent of the population has a particular disease. A test is developed for the disease. The test gives false positives 3% of the time and a false negative 2% of the time.
What is the probability that Joe tests positive?

I put 98% but that is wrong.
• May 3rd 2011, 12:29 PM
Plato
Quote:

Originally Posted by dwsmith
One half percent of the population has a particular disease. A test is developed for the disease. The test gives false positives 3% of the time and a false negative 2% of the time.
What is the probability that Joe tests positive?

$P(+)=P(+D)+P(+D^c)=P(+|D)P(D)+P(+|D^c)P(D^c)$