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

Answer:

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

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: 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?

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.9*0.16}{0.16} = 0.9$

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