SOLUTION: Suppose that 2% of convicted felons are in fact innocent. a. If a person is convicted of a felony, what is the probability that he is guilty? b. If two people are convicted of fe

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Question 1199168: Suppose that 2% of convicted felons are in fact innocent.
a. If a person is convicted of a felony, what is the probability that he is guilty?
b. If two people are convicted of felonies, what is the probability that both are guilty?
c. If three people are convicted of felonies, what is the probability that all three are guilty?
d. If four people are convicted of felonies, what is the probability that all four are guilty?
Answer by ikleyn(52778)   (Show Source): You can put this solution on YOUR website!
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Suppose that 2% of convicted felons are in fact innocent.
a. If a person is convicted of a felony, what is the probability that he is guilty?
b. If two people are convicted of felonies, what is the probability that both are guilty?
c. If three people are convicted of felonies, what is the probability that all three are guilty?
d. If four people are convicted of felonies, what is the probability that all four are guilty?
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            In this problem,  wording is  FATALLY  INCORRECT.
            It is incorrect,  because it uses self-contradictory combination of words  " convicted felons that are in fact innocent".

            First phrase  MUST  be changed - it must sound this way: 

                " Suppose that 2% of convicted    are in fact innocent. "

            Below is my solution for this  EDITED  formulation. 


(a)  ANSWER.  100% - 2% = 98% = 0.98.

     The answer follows directly the given condition: 
     2% of convicted persons are in fact innocent (given), hence the rest 100% - 2% = 98% are guilty.
     (these two categories are COMPLEMENTARY inside the set of convicted persons).


(b)  0.98*0.98 =  = 0.9604.    ANSWER


(c)   = 0.941192.              ANSWER


(d)   = 0.92236816.            ANSWER

Solved.



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