A truth serum given to a suspect is known to be 94 percent reliable when the per

Question

A truth serum given to a suspect is known to be 94 percent reliable when the person is guilty and 97 percent reliable when the person is innocent. In other words, 6 percent of the guilty are judged innocent by the serum and 3 percent of the innocent are judged guilty. If the suspect was selected from a group of suspects of which only 7 percent are guilty of having committed a crime, and the serum indicates that the suspect is guilty of having committed a crime, what is the probability that the suspect is innocent?

Explanation / Answer

probabilty of being guilty =P(G) =0.07

probabilty of being innocent =P(I) =1-0.07 =0.93

here probabilty of serum giving true positve given suspect is guilty =P(TP|G) =0.94

from above probabilty of serum giving false negative given suspect is guilty =P(FN|G) =1-0.94 =0.04

probabilty of serum giving true negative given suspect is innocent =P(TN|I) =0.97

from above probabilty of serum giving false positive given suspect is innocent =P(FP||) =1-0.97 =0.03

hence probabilty of positve result =P(P) =P(G)*P(TP|G) +P(I)*P(FP|I)

=0.07*0.94+0.93*0.03= 0.0937

therefore  probability that the suspect is innocent given serum indicates that the suspect is guilty

=P(I|P) = P(I)*P(FP|I)/P(P) =0.93*0.03/0.0937 =0.297759

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