A polygraph uses physiological indicators to determine if a person is lying or telling the truth. Assume that we have the following table of proportions of people who pass or fail the polygraph and are not lying or are lying. Note that all proportions in the table add up to 1.

(a) If a person fails the polygraph, what is the probability that they lied?

(b) If a person passes the polygraph, what is the probability that they lied?

	Fail test	pass test
not lying	0.06	0.76
lyiing	0.15	0.03