Question 1202392
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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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<pre>
This conditional probability is the ratio of two quantities


    P = {{{P(entered_a_guilty_plea_AND_was_not_sent_to_prison)/P(was_not_sent_to_prison)}}}.


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 = {{{P(entered_a_guilty_plea_AND_was_not_sent_to_prison)/P(was_not_sent_to_prison)}}} = {{{(0.5*0.65)/0.65}}} = 0.5.
</pre>

Solved.