Can you please help me with this question and show all of the work including cal
ID: 2906929 • Letter: C
Question
Can you please help me with this question and show all of the work including calculations so I can understand the process.
Crime and Punishment In a study of pleas and prison sentences, it is found that 45% of the subjects studied were sent to prison. Among those sent to prison, 40% chose to plead guilty. Among those not sent to prison, 55% chose to plead guilty. (A) If one of the study subjects is randomly selected, find the probability of getting someone 4, 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. [20 points]Explanation / Answer
Let P shows the event that person sent to prison and N shows the event that person not sent to prison. So
P(P) = 0.45
By the complement rule,
P(N) = 1 - P(P) = 0.55
Let G shows the event that person plead guilty. So
P(G|P) = 0.40, P(G|N) = 0.55
(A)
The probability ig getting someone who was not sent to prison is
P(N) = 0.55
(B)
By the Bayes theorem, the probability that person was not sent to prison given that person entered a guilty plea is,
P(N|G) = [P(G|N)P(N)] / [P(G|N)P(N)+P(G|P)P(P)] = [0.55*0.55] / [0.55*0.55 + 0.40 * 0.45] = 0.3025 / 0.4825 = 0.14595625
Answer: 0.1460