In 1982 John Hinckley was on trial, accused of having attempted to kill President Reagan. During Hinckley's trial, Dr. Daniel R. Weinberger told the court that when individuals diagnosed as schizophrenics were given CAT scans, the scans showed brain atrophy in 30% of the cases whereas when normal people were given CAT scans the scans showed brain atrophy in only 2% of the cases. Hickley's defense attorney wanted to introduce as evidence Hinckley's CAT scan, which showed brain atrophy. The defense argued that the presence of atrophy strengthened the case that Hinckley suffered from mental illness (Barnett, Greenberg, Machol 1984). Suppose the prevalence of schizophrenia in the population is 0.015. Let A ={a person has an atrophy of the brain}and S = {a person has schizophrenia} a. Find the probability that a randomly selected individual has atrophy of the brain. b. If a randomly selected individual has brain atrophy, what is the probability that the individual has schizophrenia? c. The defense was trying to make the case that Hinckley was innocent by reason of insanity (i.e., he was mentally ill). Based on the analysis you just did, if you were the judge in this case do you believe that Hinckley was mentally ill? That is, would you consider this analysis as evidence supporting the defense's position that Hinckley was mentally ill? Why or why not?