Making change probability question

[udontknowmickey]

so I originally posted this in the Math forum, then I realized there actually is a Probability forum. Like probability isn't math, but ok.


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So I was working the cash register today for my job, and this problem came to mind. (Yup, I'm a nerd, I like to think about math when I'm bored)

Lets say you had an infinite jar of coins. The probabilities of drawing out a quarter is 1/4, a dime is 1/4, a nickel is 1/4 and a penny is 1/4.

(and if anyone has issues with an infinite jar of coins, just take a jar of 4 coins, one of each, each time you draw one out you replace it. Problem is the same)

What is the expected number of coins you draw before you have exact change for a dollar?

What if the jar is finite with 100 of each?

What if the jar is finite with 4 quarters, 10 dimes, 20 nickels, and 100 pennies?

I can't seem to think of any way to solve this without brute forcing it, listing off all the possibilities of making change for a dollar and then calculating the expected draws from that. But i thought it was an interesting problem