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1. Suppose that a group of illegal counterfeiters print 1,000 copies of fake $20 bills and introduces them into the economy. Suppose that each bill is used once per week (starting in week 1), and that each time a bill is used, it has a 1 in 5 chance of being detected as fake. If it is detected, it is removed. If not, it is used again. (a) What does the expression I 1000 (O) represent? Explain. n=1 Suggestion: If you are unsure, try writing out the expression for n = 1,2,3 and consider what these might represent. (b) Find an expression of the form E an that represents the total expected number of transactions n=1 where one of the fake bills are successfully used without being detected. Then determine if your series converges or diverges, and find its sum, if possible.

1. Suppose that a group of illegal counterfeiters print 1,000 copies of fake $20 bills and introduces them into the economy. Suppose that each bill is used once per week (starting in week 1), and that each time a bill is used, it has a 1 in 5 chance of being detected as fake. If it is detected, it is removed. If not, it is used again. (a) What does the expression I 1000 (O) represent? Explain. n=1 Suggestion: If you are unsure, try writing out the expression for n = 1,2,3 and consider what these might represent. (b) Find an expression of the form E an that represents the total expected number of transactions n=1 where one of the fake bills are successfully used without being detected. Then determine if your series converges or diverges, and find its sum, if possible.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 29E
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1. Suppose that a group of illegal counterfeiters print 1,000 copies of fake $20 bills and introduces them into the economy. Suppose that each bill is used once per week (starting in week 1), and that each time a bill is used, it has a 1 in 5 chance of being detected as fake. If it is detected, it is removed. If not, it is used again. (a) What does the expression I 1000 (O) represent? Explain. n=1 Suggestion: If you are unsure, try writing out the expression for n = 1,2,3 and consider what these might represent. (b) Find an expression of the form E an that represents the total expected number of transactions n=1 where one of the fake bills are successfully used without being detected. Then determine if your series converges or diverges, and find its sum, if possible.
Transcribed Image Text:1. Suppose that a group of illegal counterfeiters print 1,000 copies of fake $20 bills and introduces them into the economy. Suppose that each bill is used once per week (starting in week 1), and that each time a bill is used, it has a 1 in 5 chance of being detected as fake. If it is detected, it is removed. If not, it is used again. (a) What does the expression I 1000 (O) represent? Explain. n=1 Suggestion: If you are unsure, try writing out the expression for n = 1,2,3 and consider what these might represent. (b) Find an expression of the form E an that represents the total expected number of transactions n=1 where one of the fake bills are successfully used without being detected. Then determine if your series converges or diverges, and find its sum, if possible.
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