Expected Insertions to Pay a Parking Meter
You need to pay $\
$ at a parking meter that only accepts quarters ($\$0.25$ each), so you need 4 real quarters to complete payment. You have an infinitely large pouch of coins where 60% are real quarters and 40% are fake.
The meter has a catch: if you insert a fake quarter, the meter resets to $\$0$ and you lose all progress. You must start over from scratch.
You draw coins one at a time from the pouch and insert them. How many coins do you expect to insert before the meter is fully paid?
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