A police interrogation handbook has suggested the following controversial proced

Question

A police interrogation handbook has suggested the following controversial procedure for attempting to get someone to admit to a crime. Stage 1: Be gentle and ask if they committed the crime Stage 2: Get more aggressive and explain to them the consequences if they are lying Stage 3: Use negative psychological techniques to make them feel guilty Interrogators are to carry out each stage in succession until the person admits to the crime. Empirical evidence suggests that while this is a good method for getting people to admit to a crime, it can also force innocent people to admit to a crime they didn't commit. The following table gives the individual admission rates for each stage, as has been determined via an investigation into the practice. Note that the probabilities only apply when a person has not admitted to the crime in all previous stages. The police know that for a particular crime, 90% of people they bring in for interrogation are guilty. Use the events G for "person is guilty" and for "person admits to the crime at step i" to answer the following questions, stating all probability rules that you use. (a) If someone admits to the crime at Step 2, what is the probability that they're guilty? (b) What is the probability that someone will admit to a crime they didn't commit?

Explanation / Answer

P(G) =0.9, P(NG )=0.1

P(G/A2) = P(A2/G) *P(G) /  [P(A2/G) *P(G)+ P (A2/NG) * P(NG)

= 0.7*0.9/ (0.7*0.9 + 0.04*0.1) = 0.993

B) Required probability = P(Remaining people in this round) * P(Ai/NG) = 1*0 +0.5 *0.04 + 0.13*0.13 = 0.0369

People in first round =1.0

Second round =1-0.5=0.5

Third round = 1-0.5-0.5(0.70+0.04)=0.13

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