I am just learning probability in my Discrete Structures class and am very lost. This is the example given in the book and I have no idea how to solve this problem.
Problem: Suppose one in 1000 people have a certain disease. Suppose medical testing is not perfect (as is the case in real life) and consequently, only 99% of the people with the disease are tested positive. Suppose 2% of the people who don’t have the disease also test positive. What is the probability of actually having the disease, given someone tests positive?
Things I do know:
- People with disease = 1/1000
- Tested positive with disease = 99/100
- People tested positive who don't have disease = 2/100
I'm not sure where to got from here with the information that I know. What are the next steps?