In 1982 John Hinckley was on trial, accused of having attempted to kill Presiden
ID: 3125615 • Letter: I
Question
In 1982 John Hinckley was on trial, accused of having attempted to kill Presiden Reagan. During Hinckley's trial, Dr. Daniel R. Weinberger told the court that when individuals diagnosed as schizophrenics were given computerized axial tomograph (CAT) scans, the scans showed brain atrophy in 30% of the cases compared with, only 2% of the scans done on normal people. Hinckley'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.
We want to know the probability that Hinckley was schizophrenic given that he had brain atrophy. Suppose approximately 1.5% of people in the United States suffer from schizophrenia. Hence P(S) = 0.015, where S means schizophrenia. We also have P(A|S) 0.3 = (A means atrophy) and P(A|S complement) = 0.02. Calculate P(S|A). Show your work.
Explanation / Answer
As
P(A) = P(S) P(A|S) + P(S') P(A|S') = 0.015*0.3 + (1-0.015)*0.02 = 0.0242
Therefore,
P(S|A) = P(S) P(A|S)/P(A) = 0.015*0.3/0.0242 = 0.185950413 [ANSWER]