# A Bonus Probability Puzzle For 2020

Our goal is to make $20.20. But … there are twists! We are given the following denominations: penny ($0.01), nickel ($0.05), dime ($0.10), quarter ($0.25), 1 dollar bill, 5 dollar bill, 10 dollar bill, and a 20 dollar bill. You are allowed to request as much of any of the denominations you want and whatever mixture of denominations you’d like provided that the total is$20.20.

Here is the first twist: You get each denomination with a certain probability. Here are the probabilities

• Penny — 99.99%
• Nickel — 99.95%
• Dime — 99.90%
• Quarter — 99.75%
• $1 bill — 99.00% •$5 bill — 95.00%
• $10 bill — 90.00% •$20 bill — 80.00%

### Challenge #2

What combination of denominations gives the highest expected value? And what is that expected value?

Don’t forget to check out these 20 puzzles for 2020!