In a study of pleas and prison sentences, it is found that 58% of the subjects s

Question

In a study of pleas and prison sentences, it is found that 58% of the subjects studied were sent to prison. Among those sent to prison. 47% chose to plead guilty. Among those not sent to prison. 38% chose to plead guilty. a. If one of the study subjects is randomly selected, find the probability of getting someone who was not sent to prison. b. If a study subject is randomly selected and it is then found that the subject entered a guilty plea, find the probability that this person was not sent to prison. a. If one of the study subjects is randomly selected, find the probability of getting someone who was not sent to prison. P(Not sent to prison) = (Type an integer or a decimal.) b. If a study subject is randomly selected and it is then found that the subject entered a guilty plea, find the probability that this person was not sent to prison. P(Not sent to prison|Guilty plea) = (Round to three decimal places as needed.)

Explanation / Answer

Given P(Prison) = 0.58 and P(Plead guilty / Prison) = 0.47

and P(Not prison) = 0.42, P(Plead quilty / not prison) = 0.38

a) P(Not presion) = 0.42

b) P(Not presion / Guilty Plea) =

= [P(Guilty Plea / Not presion) * P(Not Presion)] / {P(Guilty Plea / Not presion) * P(Not Presion) + P(Guilty

Plea / presion) * P(Presion)}

= [ 0.38*0.42 ] / {0.38*0.42 + 0.47*0.58}

= 0.1596 / 0.4322

= 0.36927

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