As a volunteer librarian, you have looked at the borrowing history of every patron of the library. From this data, you classify 75% of library patrons as "good returners" (they return books on time) and the rest as "bad returners" (they regularly return books late). Library patrons in the "bad" category allow their accounts to go overdue 50% of the time on average, whereas those in the "good" category allow their accounts to become overdue only 10% of the time. What percentage of overdue library accounts are held by library patrons in the "bad" category?
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20% |
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93.75% |
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62.5% |
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12.5% |
Ans:
P(good)=0.75
P(bad)=1-0.75=0.25
P(overdue/good)=0.10
P(overdue/bad)=0.50
So,
P(overdue)=P(overdue/good)*P(good)+P(overdue/bad)*P(bad)
=0.10*0.75+0.50*0.25
=0.20
Now,using Bayes rule,
P(bad/overdue)=P(overdue/bad)*P(bad)/P(overdue)
=0.50*0.25/0.20
=0.625 or 62.5%
As a volunteer librarian, you have looked at the borrowing history of every patron of the...
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