You might wonder: How can we assume that about 30% of the coins will be quarters, 40% will be pennies, and so on?

It comes from the assumption that when you do your shopping and you get some change, your odds of getting 24 cents, or 82 cents, or any other value, are approximately the same. Thus, we look at the coins needed to produce 99 cents (3 quarters, 2 dimes, and 4 pennies), then we look at the coins needed to produce 98 cents, then 97, all the way down to 1 cent, and add up all these coins. It turns out, when you add all these values together, you need 150 quarters, 80 dimes, 40 nickels, and 200 pennies. This is the approximate distribution of a random collection of spare change.

This doesn't work, of course, if you're the kind of person who is constantly removing the quarters from the coin jar in order to do laundry. If that is the case, you should switch from the "Simple Estimate" to the "Sample-Based Estimate" at the top of the page. This will allow you to provide an approximation of the distribution of each type of coin.