Question

suppose that 16% of crimes of this type end up in a criminal charge. this district has a false conviction rate of 5% (meaning the subject was charged but did not commit the crime) and fail to charge at a rate of 10% (meaning the person committed the crime but was not charged). if a randomly chosen suspect is charged, what is the chance that the suspect actually committed the crime

Answer 1

0.9 = 90% probability that the suspect actually committed the crime.

Explanation:

Conditional Probability

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

`P(B|A) = (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: Charged

Event B: Committed the crime.

16% of crimes of this type end up in a criminal charge.

This means that
`P(A) = 0.16`

Probability of being charged and committing the crime:

90% of 16%, so:

`P(A \cap B) = 0.9*0.16`

What is the chance that the suspect actually committed the crime?

`P(B|A) = (P(A \cap B))/(P(A)) = (0.9*0.16)/(0.16) = 0.9`

0.9 = 90% probability that the suspect actually committed the crime.