Question

A truth serum has the property that 90%90% of
the guilty suspects are properly judged while, of course,
10%10% of the guilty suspects are improperly found innocent.
On the other hand, innocent suspects are misjudged
1%1% of the time.

1. If the suspect was selected
from a group of suspects of which only 5%5% have ever
committed a crime, and the serum indicates that he is
guilty, what is the probability that he is innocent?

2. What is the probability that he is judged guilty

Answer 1

Let us denote the events

A : a randomly selected person is actually innocent

B : a randomly selected person is found to be guilty

Given

that implies P(A) = 1 - P(A^c) = 1 - 0.05 = 0.95

1. If the suspect was selected and the serum indicates that he is guilty,

The probability that he is innocent is

2. The probability that he is judged guilty