I don’t know how to handle this Statistics question and need guidance.
Consider all courtroom trials with a single defendant who is charged with a felony. Suppose that you are given the following probabilities for this situation.
Eighty-two percent of the defendants are, in fact, guilty. Given that the defendant is guilty, there is a 75 percent chance the jury will convict the person. Given that the defendant is not guilty, there is a 40 percent chance the jury will convict the person.
For simplicity, assume that the only options available to the jury are: to convict or to release the defendant.
(a) What proportion of the defendants will beconvicted by the jury?
(b) Given that a defendant is convicted, whatis the probability the person is, in fact, guilty?
(c) What is the probability that the jury willmake a correct decision?
(d) Given that the jury makes an incorrect decision, what is the probability that the decision is to release a guilty person?