3. Suppose a particular crime is committed in Jerry\'s apartment. We\'d like to

Question

3. Suppose a particular crime is committed in Jerry's apartment. We'd like to know whether Newman is guilty of the crime. We are torn as to whether we think he is guilty: we think it's equally likely that he guilty or not guilty. Suppose that, in similar situations, we know that if a suspect is guilty, 85% of the time their finger prints are found at the scene, and, we know that if a suspect is not guilty, 30% of the time their finger prints are found at the scene. (a) What is the probability that Newman's finger prints are found at the scene? (b) If Newman's finger prints are found at the scene, how likely is it that he is guilty? (c) If Newman's finger prints are not found at the scene, how likely is it that he is guilty?

Explanation / Answer

Ans:

Given that

P(guilty)=P(not guilty)=0.5

P(finger prints found/guilty)=0.85

P(finger prints not found/guilty)=1-0.85=0.15

P(finger prints found/not guilty)=0.3

a)

P(finger prints found)=P(finger prints found/guilty)*P(gulty)+P(finger prints found/not guilty)*P(not guilty)

=0.85*0.5+0.3*0.5

=0.575

b)P(guilty/finger prints are found)=P(finger prints are found/guilty)*P(guilty)/P(finger prints are found)

=(0.85*0.5)/0.575=0.7391

c)P(guilty/finger prints are not found)=P(finger prints are not found/guilty)*P(guilty)/P(finger prints are not found)

=(0.15*0.5)/(1-0.575)

=0.1765

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