Question

A lie detector is known to be 4/5 reliable when the person is guilty and 9/10 reliable when the person is innocent. If a suspect is chosen from a group of suspects of which only 1/100 have ever committed a crime, and the test indicates that the person is guilty, what is the probability that he is guilty?

Answer 1

Answer:

0.0748 = 7.48% probability that he is guilty

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Tests indicates guilty

Event B: Person is guilty

Probability that the test indicates that the person is guilty:

4/5 = 0.8 of 1/100 = 0.01(person is guilty)

1 - 0.9 = 0.1 of 1 - 0.99(person is not guilty). So

$P(A) = 0.8*0.01 + 0.1*0.99 = 0.107$

Test indicates guilty and the person is guilty;

0.01 of 0.8. So

$P(A \cap B) = 0.01*0.8 = 0.008$

What is the probability that he is guilty?

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.008}{0.107} = 0.0748$

0.0748 = 7.48% probability that he is guilty