A lie detector shows a positive reading 10% of the time given that the person is telling the truth and 95% given the person is lying. Suppose that there is a suspect who is denying the the crime and there is a 50% chance that the person comitted the crime.
A. what is the probability that the test gives a positive reading?
B. A test is randomly taken: What is the probability that the person did not commit the crime given that the test indicates a negative reading.
The Attempt at a Solution
A. I did a tree diagram and resulted in summing 10% of 50% and 95% of 50% and received a return of 52.5%. Is this acceptable?
B. I did another tree diagram and summed the inverse. 90% of 50% and 5% of 50% and received a return of 47.5%