UIUC STAT 400 - Week 3 ‐ Discussion Questions

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Week 3 Discussion Questions STAT 400 D Unger Table of Contents Exercise 1 Conditional Probability Exercise 1 Conditional Probability 1 Exercise 2 DeMorgan s Law Conditional Probability 1 Exercise 3 DeMorgan s Law Conditional Probability 1 Exercise 4 Conditional Probability 2 Exercise 5 Independence 2 Exercise 6 Independence 2 Exercise 7 Independence 2 If P A 0 7 P B 0 5 and P A B 0 1 then find the following c P B A a P A B If P B 0 45 P A B 0 67 and P A B 0 89 then find the following c P B A a P A a Given that P A B 0 76 and P A B 0 87 find P A b Suppose also that P B 0 20 Find the following i P A B iii P B A b P A B b P A B Exercise 3 DeMorgan s Law Conditional Probability Exercise 2 DeMorgan s Law Conditional Probability ii P A B Exercise 5 Independence Exercise 4 Conditional Probability Gringotts 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 The probability that a randomly selected student at Faber College owns a bicycle is 0 55 the probability that a student owns a car is 0 30 and the probability that a student owns both is 0 10 Are the events of a student owns a bicycle and a student owns a car independent Amazon Prime delivers a package to the wrong address with probability 0 02 on any delivery Suppose that each delivery is independent of all the others One driver had 7 packages to deliver on a particular day What is the probability that at least one package was delivered to the wrong address A major oil company has decided to drill independent test wells in the plains of Texas The probability of any well producing oil is 0 30 Find the probability that the fourth well is the first to produce oil Exercise 7 Independence Exercise 6 Independence

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# UIUC STAT 400 - Week 3 ‐ Discussion Questions

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