Week 4 Assignment

Week 4 Assignment Did the subject actually lie? Total No (did not lie) Yes (did lie) The polygraph test indicated that the subject lied. 15 42 57 The polygraph test indicated that the subject did not lie. 32 9 41 Total 47 51 98 1. If one of the subjects is randomly selected, find the probability of selecting someone who lied. P ( somoenwho lied ) = numberof subjects who lied Totalnumber of subjects = 42 98 = 0.4286 ¿ 0.4286 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. P ( did not lie ∧ polygraphindication of not lying ) = 32 98 = 0.3265 ¿ 0.3265 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. P ( lied ∨ polygraphindicativeof not lying ) = P ( lied )+ P ( polygraph indicativeof not lying )− P ( lied ∧ polyg ¿ 51 + 41 − 9 98 = 83 98 = 0.8469 ¿ 0.8469 4. If two different subjects are randomly selected without replacement, find the probability that they both lied. P ( bothlied ) = P ( first subject lied ) ×P ( second subject lied ) = 51 98 × 50 97 = 0.2683 ¿ 0.2683 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.