33 In a study of pleas and prison sentences it is found that

3.3. In a study of pleas and prison sentences, it is found that 40% of the subjects studied were sent to prison. Among those sent to prison, 20% chose to plead guilty. Among those not sent to prison, 10% chose to plead guilty. 3.3.a (0.5 pt) If a study subject is randomly selected, what is the probability that this person was not sent to prison? 3.3.b (0.5 pt) If a study subject is randomly selected, what is the probability that this study subject entered a guilty plea? 3.3.c (0.5 pt) if a study subject is randomly selected amid it is then found that this subject entered a guilty plea, find the probability that this person was not sent to prison.

Solution

Consider total no.of samples(pleas) be 100
Sent to prison are 40 In this guilty are 20
Not sent are 60 in this guilty are 10
a) probability person not sent to prison is 60/100=.6
b) probability of guilty plea is (20+10)/100=.3
c) probability of guilty not sent to prison is 10/100=.1