Question

A thief who is particularly knowledgeable about statistics and the legal system determines that if he commits a given heist the probability that he is never caught is 60%. If he is arrested he will go to trial where there is a 30% chance the jury will acquit him, a 30% chance he is convicted and serves a prison sentence less than five years, and a 40% chance the sentence is more than five years.

What is the probability that the thief is not imprisoned in 5 years?

What is the probability that the thief was arrested given that he is not imprisoned in 5 years?

Answer 1

9514 1404 393

Answer:

about 28.6%

Explanation:

The conditional probability equation can be used:

P(arrested | not in jail) = P(arrested & not in jail)/P(not in jail)

= 0.24/0.84 = 2/7 ≈ 28.6%