SOLUTION: A non-governmental organization (NGO) conducts a study on human rights for a group of people who are on trial. The organization found that 45% of the them were sent to prison. Am

Question 1181943: A non-governmental organization (NGO) conducts a study on human rights for a group of people
who are on trial. The organization found that 45% of the them were sent to prison. Among those
sent to prison, 25% chose to plead guilty. Among those not sent to prison, 80% chose to plead
guilty.
(a) If the NGO randomly selects one of them and it is then found that he or she has entered a
guilty plea, find the probability that this person was not sent to prison.
(b) If the NGO randomly selects one of them and it is then found that he or she has entered
without guilty plea, find the probability that this person was not sent to prison.
(c) If a person does not want to be sent to prison, how would the NGO advise this person
according to your findings in (a) and (b)
Answer by mathmate(429) (Show Source): You can put this solution on YOUR website!
A1181943 (2021-06-15 00:21:32): A non-governmental organization (NGO) conducts a study on human rights for a group of people who are on trial. The organization found that 45% of the them were sent to prison. Among those sent to prison, 25% chose to plead guilty. Among those not sent to prison, 80% chose to plead guilty.
(a) If the NGO randomly selects one of them and it is then found that he or she has entered a
guilty plea, find the probability that this person was not sent to prison.
(b) If the NGO randomly selects one of them and it is then found that he or she has entered
without guilty plea, find the probability that this person was not sent to prison.
(c) If a person does not want to be sent to prison, how would the NGO advise this person
according to your findings in (a) and (b)

Solution:
Define events:
P = prison, ~P = no prison
G = pleaded guilty, ~G = did not plead guilty

Draw up a contingency table

Plea------Prison----no prison
Guilty----11.25%----11%
~guilty---33.75%----44%

(a)
Probability that person was not sent to prison after he pleaded guilty
= P( ~P | G )
= P( ~P and G ) / P(G)
= 11%/(11.25%+11%)
= 11/(11.25+11)
= 11/22.25
= 49.4%

(b)
Probability that person was not sent to prison after he pleaded not guilty
= P( ~P | ~G )
= P(~P and ~G) / P(~G)
= 44% / (44%+33.75%)
= 44/(44+33.75)
= 56.6%

(c)
From (a) and (b), if NGO has reason to believe that all cases are treated randomly irrespective of circumstances, it would advise the client to plead not guilty since it has a slightly higher probability (56.6%) of not going to prison over pleading guilty (49.4%).

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