Clothes shopping!

You are shopping at the hottest new fashion outlet in town. While in the check-out line, you reach in your pocket and realize that in addition to your dollar bills, you have a quarter, dime, nickel, and two pennies. What is the probability that you will not be able to exactly match the change part of your bill with the 5 coins in your pocket?

Details and assumptions

Please write your answer in decimal form, rounded (if necessary) to the nearest hundredth.

A note on the source

This problem was taken from the Ole Miss Math Contest, which was hosted by Dr. David Rock of The University of Mississippi; the contest has not been so active recently and will probably be on hiatus for the foreseeable future. This problem was taken from the 'Algebra in Action' Challenge Mode section.

Image source: Wojtek Witkowski, via Unsplash archive


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