Use the data in the following table that shows results from a polygraph (lie detector) conducted by researchers Charles R. Honts and Gordon H. Barland. In each case, it was known if the subjects lied or did not lie, so the table indicates when the polygraph was correct.

	Did the subject actually lie?
No (did not lie)	Yes (did lie)
The polygraph test indicated that the subject lied.	15	42
The polygraph test indicated that the subject did not lie.	32	9

1. If one of the subjects is randomly selected, find the probability of selecting someone who lied.
2. If one of the subjects is randomly selected, find the probability of selecting someone who did not lie and had a polygraph indication of not lying.
3. If one of the subjects is randomly selected, find the probability of selecting someone who lied or had a polygraph indicative of not lying.
4. If two different subjects are randomly selected without replacement, find the probability that they both lied.

5. Use subjective probability to estimate the probability of randomly selecting a subject who did not lie and whose polygraph indicated that he or she did lie.