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STAT 400
Spring 2011
Homework #2
(10 points)
(due Friday, February 4, by 3:00 p.m.)
No credit will be given without supporting work.
1.
A bank classifies borrowers as "high risk" or "low risk," and 16% of its loans are
made to those in the "high risk" category.
Of all the bank's loans, 5% are in default.
It is also known that 40% of the loans in default are to highrisk borrowers.
a)
What is the probability that a randomly selected loan is in default and issued to a
highrisk borrower?
b)
What is the probability that a loan will default, given that it is issued to a highrisk
borrower?
c)
What is the probability that a randomly selected loan is either in default or issued to
a highrisk borrower, or both?
d)
A loan is being issued to a borrower who is not highrisk. What is the probability
that this loan will default?
e)
Are events {a randomly selected loan is in default} and {a randomly selected
loan is issued to a highrisk borrower} independent?
Justify your answer
.
2.
At
Initech
, 50% of all employees surf the Internet during work hours.
20% of the
employees surf the Internet and play
Solitaire
during work hours.
It is also known
that 60% of the employees either surf the Internet or play
Solitaire
(or both) during
work hours.
a)
What proportion of the employees play
Solitaire
during work hours?
b)
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 Spring '08
 Kim

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