Question

ons 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 0.91, and the probability the defendant is acquitted, given innocence, is 0.91. Suppose that 95% of all defendants truly are guilty. Given that the defendant is convicted, find the probability he or she was actually innocent ordi The probability is ceri (Type an integer or a decimal. Round to the nearest thousandth as needed.) ibu b. Repeat part a, but under the assumption that 50% of all defendants truly are guilty. wer: The probability is soli (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 0.99, and the probability the defendant is acquitted, given innocence, is 0.75 erdi Suppose that 85% of all defendants truly are guilty. Given that the defendant is convicted, find the probability he or she was actually innocent. bu The probability is (Type an integer or a decimal. Round to the nearest thousandth as needed) cer ol

Answer 1

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let A= defendant is acqu is acquitted cz 11 Convicted. G 11 guilty I 21 innocenti C a) G PG 309) & PLA112 0.91 & PCG) 0.95 To find, P(C) PCCI). PCI) PO (1-P(AD) (1-P10) PTC11).(1) +PC916) (6) 0-91) x (0.05 1-0.91) 0.91) R0.05 + 0.91*0.95

0.005.17 20 0.005 Ans) change js > 0-5o. (T)=0-50 PL 1) (1-0,91) 0.5 (1-0-9 10-5+ 0.9 120.5 -og (Ans ) PC C167 -0.99, PAI ) 20.75 PCG)20-85 m PCI) = 0.15 PEIT) PLC II) x PCI) Pall) f(I) + P(EG) Plbs) 0.15 0.0 990:15 0.99 ao 15 to 9980085 (ARS)