# How would I solve a classic Bayes Theorem problem using a probability tree? To help visualize what Bayes Theorem is doing.

For example

Assume that a test for a disease gives a positive result for 2.5% of people who do not have the disease, but does not test negative if the person has the disease.

What is the probability that a person who tested positive has the disease if 3% of people have the disease?

With Bayes theorem, we could technics listed here http://sphweb.bumc.bu.edu/otlt/MPH-Modules/BS/BS704_Probability/BS704_Probability6.html.

But how would you solve the noted problem only using a probability tree? I want to know how because it will help me visualize how Bayes Theorem is working in a different abstraction.

As I have heard ALL Probabilities can be solved with probabilities trees. I would like to see the computation done in Bayes Theorem solved/expanded into a probability tree.

• 1. Yes, probabilities should sum to $1$ ($100\%$) where the branches split. 2. Sorry, I had a typo in there, it should have been $.5530$ and not $.5330$ as in the calculation in the $1$ st diagram. $\frac{.03}{.05425} = .5530$ – Phil H Oct 22 '18 at 17:05