In a criminal trial in the United? States, it must be proven that a defendant is
ID: 3368176 • Letter: I
Question
In a criminal trial in the United? States, it must be proven that a defendant is guilty beyond a reasonable doubt. In a civil? trial, it must only be proven by a preponderance of the evidence that a defendant is guilty. Complete parts a through c below.
a. In a criminal trial by? jury, suppose the probability the defendant is? convicted, given? guilt, is 0.930?, and the probability the defendant is? acquitted, given? innocence, is 0.930
Suppose that 84?% of all defendants truly are guilty. Given that the defendant is? convicted, find the probability he or she was actually innocent.
The probability is ?
?(Type an integer or a decimal. Round to the nearest thousandth as? needed.)
b. Repeat part? a, but under the assumption that 50?% of all defendants truly are guilty.The probability is ?
?(Type an integer or a decimal. Round to the nearest thousandth as? needed.)
c. In a civil? trial, suppose the probability the defendant is? convicted, given? guilt, is 0.97?, and the probability the defendant is? acquitted, given? innocence, is 0.72. Suppose that 85?% of all defendants truly are guilty. Given that the defendant is? convicted, find the probability he or she was actually innocent.
The probability is?
?(Type an integer or a decimal. Round to the nearest thousandth as? needed.)
The probability is The probablityExplanation / Answer
a) P(Defendent is convicted) =0.93
P(Defendent is acquitted)= 0.93
84% of people found gulity.
P(He or she actually innocent) = P(Innocent found gulity) / P(defenders found gulity)
P(Not gulity) =1- P(Found gulity)= 1-0.84= 0.16
P(Innocent found gulity)= (1- P(defendent convicted)* P(Not gulity)= 0.16* (1-0.93)= 0.0112
P(Defenders found gulity)= 0.84*0.93+ 0.0112= 0.7924
P(He or she actually innocent) = P(Innocent found gulity) / P(defenders found gulity) = 0.0112/ 0.7924= 0.014134
b)
P(Defendent is convicted) =0.93
P(Defendent is acquitted)= 0.93
50% of people found gulity.
P(He or she actually innocent) = P(Innocent found gulity) / P(defenders found gulity)
P(Not gulity) =1- P(Found gulity)= 1-0.50= 0.50
P(Innocent found gulity)= (1- P(defendent convicted)* P(Not gulity)= 0.50* (1-0.93)= 0.035
P(Defenders found gulity)= 0.50*0.93+ 0.035= 0.5
P(He or she actually innocent) = P(Innocent found gulity) / P(defenders found gulity) = 0.035/0.50=0.07
c) P(Defendent is convicted) =0.97
P(Defendent is acquitted)= 0.72
85% of people found gulity.
P(He or she actually innocent) = P(Innocent found gulity) / P(defenders found gulity)
P(Not gulity) =1- P(Found gulity)= 1-0.85= 0.15
P(Innocent found gulity)= (1- P(defendent convicted)* P(Not gulity)= 0.15* (1-0.72)= 0.042
P(Defenders found gulity)= 0.85*0.97+ 0.042= 0.8665
P(He or she actually innocent) = P(Innocent found gulity) / P(defenders found gulity) = 0.042/ 0.8665= 0.048471