2 stats problems

Homework 2

1. The U.S. Bureau of Justice released the following probabilities for those arrested for committing various felony crimes in the United States

Probability of Being
Crime	Prosecuted	Convicted	Jailed for >1 Year
Homicide Assault Burglary Arson Drug Offenses Weapons Public Disorders	0.91 0.79 0.88 0.88 0.78 0.83 0.92	0.75 0.64 0.81 0.72 0.69 0.70 0.85	0.73 0.15 0.28 0.28 0.19 0.13 0.12

David has been arrested for Homicide, Bill has been arrested for a weapon offense, and Dan has been arrested on burglary. Assuming these individuals are typical perpetrators and the decisions regarding their respective fates are unrelated, determine the probability that: (10 points)

(A) David will be jailed for more than a year

(B) Either David or Bill (or both) will be convicted

(C) None of the three will be jailed for more than a year

(D) David and Bill will be convicted, but Dan will be found innocent

(E) None will be prosecuted

2. A construction company has bid on two contracts. The probability of winning contract A is 0.3. If the company wins contract A, then the probability of winning contract B is 0.4. If the company loses contract A, then the probability of winning contract B deceases to 0.2. Find the probability of the following events (10 points)

(A) Construct a tree diagram for this problem

(B) Compute the probability of winning both contacts, that is,

(C) Compute the probability of winning exactly one contract, that is,

(D) Winning at least one contract, that is,