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.
Best Answer
A tree diagram still needs use of the formula to determine a conditional probability. My attempt here identifies the different combinations of outcomes the same as a table.
The diagram below is a more formal presentation, but again, without a formula or explanation of how to arrive at the values, I don't think it helps with conceptual understanding any more than a table.