The eyewitness is .9 reliable. The probability that the defendant committed the crime, given the eyewitnesses...
The eyewitness is .9 reliable. The probability that the defendant committed the crime, given the eyewitnesses testimony is .85 (the posterior probability). What was the prior probability that the defendant was guilty?
Homework Answers
let P(guilty)=x
P(eyewitness testimony guiltY)=P(guilty)*P(eyewitness testimony guilty|guilty)+P(not guilty)*P(eyewitness testimony guilty|not guilty)
therefore P(guilty|eyewitness testimony guiltY)=
P(guilty)*P(eyewitness testimony guilty|guilty)/P(eyewitness testimony guiltY)
0.85=x*0.9/(x*0.9+(1-x)*(1-0.9))
0.68*x+0.085 =0.9*x
x =0.3864= prior probability that the defendant was guilty
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