I need someone's help with an assignment, I'm not sure what I'm doing is correct, and would love if someone else could take a look!
"Professor James Duane from Regent University, USA advocates for constant execution of the right to remain silent and immediately calling the lawyer every time a person is questioned by the police on any topic. He has a popular YouTube lecture "Don’t talk to the Police" and the book "You Have the Right to Remain Innocent". Let’s try to probabilistically evaluate his claims using the following model.
We have individuals with no history of convictions (person NC) and with a history of convictions (person C). Suppose:
- 1) If any person remains silent, there is a 0.001 risk of his case ending up in the court.
- 2) If a person NC talks to the police, there is a 0.002 risk of the police using his words against him and his case ending up in the court.
- 3) If a person C talks to the police, there is a 0.005 risk of the police using his words against him and his case ending up in the court.
- 4) The probability of not being convicted in the court are 0.5 for person NC and 0.1 for person C.
- 5) The probability of not being convicted drops 4 times if a person did not talk to the police during the investigation, as the jury thinks he has something to hide.
- 6) If a person is convicted and talked to the police during the investigation, his sentence is reduced by 0.75 factor as he is considered cooperative.
The police arrested a person suspecting he is involved in a certain crime. The penalty for the crime is 5 years in prison."
Questions:
- a) A person has no history of convictions. What are the expected mean sentence durations he will have to spend in prison if he talks to the police or remains silent?
- b) A person has a history of convictions. What are the expected mean sentence durations he will have to spend in prison if he talks to the police or remains silent?
My answer to a)
NC talks:
P(A) = 0.002 (NC talks)
P(B) = 0.5 (NC gets convicted)
P(A and B) = P(A) * P(B) = 0.002*0.5 = 0.001
Sentence is reduced by 0.75 if you don't talk (5*0.75=3.75), so NC not talking to the police yields a conditional risk at 0.001 and a 3.75 year sentence.
NC doesn't talk:
P(A) = 0.001 (NC remain silent)
P(B) = 0.5 (NC gets convicted)
P(A and B) = 0.001*0.5=0.005
Conviction risk increases by 4 (has something to hide), 4*0.0005=0.002.
Expected mean value: Here I'm not sure, I would do (0.001 risk * 3.75 years) + (0.002 risk * 5 years) = 0.01375.