SOLUTION: In a study of pleas and prison sentences, it is found that 35% of the subjects studied were sent to prison. Among those sent to prison, 30% chose to plead guilty. Among those not s
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Question 1202392: In a study of pleas and prison sentences, it is found that 35% of the subjects studied were sent to prison. Among those sent to prison, 30% chose to plead guilty. Among those not sent to prison, 50% chose to plead guilty.
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. Answer by ikleyn(52775) (Show Source):
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In a study of pleas and prison sentences, it is found that 35% of the subjects studied
were sent to prison. Among those sent to prison, 30% chose to plead guilty.
Among those not sent to prison, 50% chose to plead guilty.
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.
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This conditional probability is the ratio of two quantities
P = .
The denominator is P(was_not_sent_to_prison) = 1 - 0.35 = 0.65.
The numerator is P(entered_a_guilty_plea_AND_was_not_sent_to_prison) = 0.5*(1-0.35) = 0.5*0.65.
The answer is P = = = 0.5.
