STAT 400 Spring 2015 Discussion 2 1 Of the students who have an internship with Veridian Dynamics 40 are seniors 30 are juniors 20 are sophomores and 10 are freshmen At the end of each semester the student interns are evaluated 20 of the seniors receive Exceeds Expectations EE rating so do 24 of juniors 30 of sophomores and 38 of freshmen The longer you have your internship the more difficult it is to earn EE rating a If a student intern selected at random has EE rating what is the probability he she is a senior b If a student intern selected at random does not have EE rating what is the probability he she is not a senior c At the end of the semester student interns who either are seniors or have EE rating or both receive a coffee mug as a bonus What proportion of the student interns would receive a coffee mug 2 The population of Lilliput is divided into Little Endians and Big Endians based on which end of a boiled egg they believe should be opened Suppose that 60 of Lilliputians are Little Endians and 40 are Big Endians Suppose also that 16 of Little Endians and 26 of Big Endians have blue eyes a What proportion of Lilliput population have blue eyes b You meet a Lilliputian with blue eyes What is the probability that he is a Little Endian c What is the probability that a Lilliputian is a Big Endian if his eyes are not blue d The first democratically elected Lilliputian president is a Little Endian with blue eyes His first day in office he proposed a tax break for Lilliputians who are either Little Endians or have blue eyes or both What proportion of the Lilliput population would receive a tax break under his proposal 3 Jack Mike and Tom are roommates and every Sunday night they split a large pizza for dinner When there is only one slice left the probability that Jack wants it is 0 40 the probability that Mike wants it is 0 35 and the probability that Tom wants it is 0 25 Suppose that whether or not each one of them will want the last slice is independent of the other two a What is the probability that only one of the roommates will want the last slice b What is the probability that at least one of the roommates will want the last slice c What is the probability that at most one of the roommates will want the last slice 4 Suppose that 70 of all customers at a particular store have a Visa credit card and 50 of all the customers have an American Express credit card It is also known that 40 of the customers who have Visa also have American Express a What is the probability that a randomly selected customer would have either a Visa credit card or an American Express credit card or both b Given that a randomly selected customer has an American Express credit card what is the probability that they have a Visa credit card c Are events a customer has a Visa credit card and a customer has an American Express credit card independent 1 Of the students who have an internship with Veridian Dynamics 40 are seniors 30 are juniors 20 are sophomores and 10 are freshmen At the end of each semester the student interns are evaluated 20 of the seniors receive Exceeds Expectations EE rating so do 24 of juniors 30 of sophomores and 38 of freshmen The longer you have your internship the more difficult it is to earn EE rating P Sr 0 40 P Jr 0 30 P EE Sr 0 20 P So 0 20 P EE Jr 0 24 P Fr 0 10 P EE So 0 30 P EE Fr 0 38 a If a student intern selected at random has EE rating what is the probability he she is a senior Law of Total Probability P EE P Sr P EE Sr P Jr P EE Jr P So P EE So P Fr P EE Fr 0 40 0 20 0 30 0 24 0 20 0 30 0 10 0 38 0 25 Bayes Theorem P Sr EE P Sr P EE Sr 0 40 0 20 0 08 P Sr EE 0 32 0 25 0 25 P EE P EE Sr Jr So Fr EE 0 08 0 072 0 06 0 038 0 25 EE 0 32 0 228 0 14 0 062 0 75 0 40 0 30 0 20 0 10 1 00 b If a student intern selected at random does not have EE rating what is the probability he she is not a senior P Sr EE c P Sr EE P EE 0 43 0 228 0 14 0 062 43 0 57333 0 75 0 75 75 At the end of the semester student interns who either are seniors or have EE rating or both receive a coffee mug as a bonus What proportion of the student interns would receive a coffee mug P Sr EE P Sr P EE P Sr EE 0 40 0 25 0 08 0 57 2 The population of Lilliput is divided into Little Endians and Big Endians based on which end of a boiled egg they believe should be opened Suppose that 60 of Lilliputians are Little Endians and 40 are Big Endians Suppose also that 16 of Little Endians and 26 of Big Endians have blue eyes P Little 0 60 a P Big 0 40 P Blue Little 0 16 16 of Little Endians have blue eyes P Blue Big 0 26 26 of Big Endians have blue eyes What proportion of Lilliput population have blue eyes Blue Blue Little 0 60 0 16 0 096 0 504 0 60 P Blue Little 0 16 Big 0 40 0 26 0 104 0 296 0 40 P Blue Big 0 26 0 20 0 80 1 00 OR P Blue P Little P Blue Little P Big P Blue Big 0 60 0 16 0 40 0 26 0 096 0 104 0 20 b You meet a Lilliputian with blue eyes What is the probability that he is a Little Endian P Little Blue c What is the probability that a Lilliputian is a Big Endian if his eyes are not blue P Big Blue d P Little Blue 0 096 0 48 P Blue 0 20 P Big Blue 0 296 0 37 0 80 P Blue The first democratically elected Lilliputian president is a Little Endian with blue eyes His first day in office he proposed a tax break for Lilliputians who are either Little Endians or have blue eyes or both What proportion of the Lilliput population would receive a tax break under his proposal P Little Blue P Little P Blue P Little Blue 0 60 0 20 0 096 0 704 OR P Little Blue P Little Blue P Little Blue P Big Blue 0 096 0 504 0 104 0 704 OR P Little …
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