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.
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.
Suppose that a new detection tool is introduced starting in week 3 and that from week 3 onwards,
each fake bill has a 1 in 3 chance of being detected at each transaction. In this case, what is the total
expected number of times that the fake bills are successfully used in transactions without being detected?
Suggestion: Start by writing expressions for the expected number of undetected transactions in week 1,
week 2, week 3, week 4, etc. and think about ways to write all or part of this as a series.
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