Suppose 97% of the population are law abiding citizens, and the remaining citizens break the law. If an innocent person is arrested, they have a 10% chance of confessing, whereas a guilty personconfesses 45% of the time. What is the probability that a person who confessed to a crime is guilty

12.22% probability that a person who confessed to a crime is guilty

Step-by-step explanation:

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

In which

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

is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question, we have that:

Event A: Confessing

Event B: Being guilty

Probability of confessing:

10% of 97%(non-guilty) or 45% of 3%(guilty). So

Confessing and being guilty:

3% are guilty, and of those, 45% confess. So

What is the probability that a person who confessed to a crime is guilty?

12.22% probability that a person who confessed to a crime is guilty