In a study of pleas and prison sentences. it is found that 65% of the subjects s

Question

In a study of pleas and prison sentences. it is found that 65% of the subjects studied were sent to prison. Among those sent to prison 44% chose to plead guilty. Among those not sent to prison, 32% chose to plead guilty. a. one of the study subjects is randomly selected, find the probability of getting someone who was not sent to prison. b. lf a study subject is randomly selected and it is then found that the subject entered a guilty plus find the this person was sent a. If one of the study subjects is randomly selected, find the probability of gazing 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 this person was not sent to prison P(Not sent to prison Guilty plea) = Round to tree decimal places as needed.)

Explanation / Answer

Population is x

Then percentage went to prison is 0.65x

Percentage plead guilty among those who were sent to prison are 0.44*0.65x

Percentage pleading guilty among those who wasn’t sent to prison are 0.32*0.35x

Probability of getting someone not sent to prison is 0.35

For b we will use conditional probability theorem

Probability of event A when B has happened is given by

P(A/B) = P(B/A) / P(B)

B : Person entered a guilt plea

A : Person was not sent to prison

P(B) = (0.44*0.65) + (0.35*0.32)

P(B/A) = 0.32*0.35

Putting these values above gives our answer

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