Question

A lie detector test is accurate 70% of the time, meaning that for 30% of the times a suspect is telling the truth, the test will conclude that the suspect is lying, and for 30% of the times a suspect is lying, the test will conclude that he or she is telling the truth. A police detective arrested a suspect who is one of only four possible perpetrators of a jewel theft. If the test result is positive (i.e., concludes that the subject is guilty), what is the probability that the arrested suspect is actually guilty

Answer 1

0.475

Explanation:

Given that :

We are to calculate the true positive :

True POSITIVE (TP) = 70% = 0.7

False POSITIVE (CP = 30% = 0.3

True Negative = 30% = 0.3

Number arrested = 4

(1/n * TP) / [(1/n * TP) + (n-1 /n * FP)

= (1/4 * 0.7) / [(1/4 * 0.7) + (3/4 * 0.3)

= 0.175 / (0.175 + 0.225)

= 0.175 / 0.4

= 0.475