Answer the following questions using Bayes\' rule, p(AB) = p BA ABIA PAA NA) 7.1

Question

Answer the following questions using Bayes' rule, p(AB) = p BA ABIA PAA NA) 7.1 Suppose you are a judge hearing a criminal appeal. Before looking into the facts of the case, you would like to get a sense of how likely it is that a given defendant was wrongfully convicted at trial. You know that trial juries are not perfect. They only convict guilty defendants 90% of the time, and wrongly convict innocent defendants 10% of the time. You also assess that 80% of the defendants who are brought to trial are actually guilty of their crimes. What is the probability that a particular defendant is really innocent, given that he or she was convicted by a jury?

Explanation / Answer

probability of convicted by jury =P(inncent and convicted+guilty and convicted)

=0.2*0.1+0.8*0.9=0.74

threfore probability of a defender to be innocent given convicted =P(inncent and convicted)/P(convicted)

=0.2*0.1/0.74=0.0270

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