The U.S. Bureau of Justice released the following probabilities for those arrest
ID: 3237592 • Letter: T
Question
The U.S. Bureau of Justice released the following probabilities for those arrested for committing various felony crimes in the United States
l. 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 Convicted Crime Prosecuted Jailed for 1 Year Homicide 0.91 0.75 0.73 Assault 0.64 0.15 0.79 0.28 Burglary 0.88 0.81 Arson 0.88 0.72 0.28 0.19 Drug Offenses 0.78 0.69 Weapons 0.83 0.70 0.13 0.12 Public Disorders 0.92 0.85 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 prosecutedExplanation / Answer
(A) Probability that David will be jailed for more than a year = 0.73, since David is arrested for Homicide.
(B) P(Either David or Bill is will be convicted) = P(David will be convicted) + P(Bill will be convicted) - P(David and Bill will be convicted)
= 0.75 + 0.70 - 0.75*0.70
= 1.45 - 0.525
= 0.925
(c) P(None of three will be jailed for more than a year) = (1-0.73)*(1-0.28)*(1-0.13)
= 0.27*0.72*0.87
= 0.169128
(D) P(David and Bill will be convicted, but Dan will be innocent) = 0.75*0.70*(1-0.81)
= 0.75*0.70*0.19
= 0.09975
(e) P(None will be procecuted) = (1-0.91)*(1-0.88)*(1-0.83)
= 0.09*0.12*0.17
= 0.001836
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