A polygraph machine detects lies 65% of the time. But it incorrectly flags the true statement as a lie 15% of the time.
a. Suppose a test subject will lie 10% of the time. What is the probability that a random statement by the subject will be flagged as a lie by the machine?
b. If another subject makes a statement that the machine flags as a lie, what is the probability that it really was a lie?