Polygraph tests (lie-detector tests) are often routinely administered to employees or prospective employees in sensitive positions. A polygraph test will label subjects + (positive) if it determines the subject is lying and - (negative) if it determines the subject is not lying. Subjects can either be lying or not lying (truthful).

According to studies of polygraph reliability, the probability that the polygraph will test + (positive) given/conditional that the subject is actually lying is 0.88. The probability that the polygraph will test (negative) given the subject is telling the truth (not lying) is 0.84. Assume that 90% chance a subject is telling the truth (10% chance of lying).

a. What is the probability that the polygraph returns a + (positive) label?

b. Say the polygraph test labels someone + (positive). What is the probability this subject is actually lying?

c. Is the polygraph label independent from whether the subject is lying or not?