# 400Hw02 - STAT 400 Spring 2011 Homework#2(10 points(due...

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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 high-risk borrowers. a) What is the probability that a randomly selected loan is in default and issued to a high-risk borrower? b) What is the probability that a loan will default, given that it is issued to a high-risk borrower? c) What is the probability that a randomly selected loan is either in default or issued to a high-risk borrower, or both? d) A loan is being issued to a borrower who is not high-risk. 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 high-risk 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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## This note was uploaded on 02/24/2011 for the course STAT 400 taught by Professor Kim during the Spring '08 term at University of Illinois, Urbana Champaign.

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400Hw02 - STAT 400 Spring 2011 Homework#2(10 points(due...

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