Here's a simple problem from a prep book I'm using to get ready for a test.
A polygraph test is 90% effective in determining if someone is lying. However, it has a 10% error-rate for "false" detection. A congressman who is known to lie 25% of the time is tested and found to be telling the truth.
A. What is the probability that he could still be lying? (note that the correct answer here is supposed to be 3.6%, a number I cannot derive).
B. If the polygraph test says he is lying, what is the probability that he could actually be telling the truth?