Answer the following questions using Bayes' rule: p(A|B) = p(B|A)p(A) p(B|A)p(A)+p(B|A)p(A)

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?