The expected value is simply the average of the values of all of the bills.
The expected value is the sum of the values of each bill times the probability that that bill is drawn.
There are 5 bills, 1, 5, 10, 20, 100.
The probability of drawing one of the bills out of a hat is 1 out of 5, or 1/5.
The expected value then is:
EV = (1/5) * $1 + (1/5) * $5 +(1/5) * $10 +(1/5) * $20 +(1/5) * $100
Rewriting, you can see that in this problem, EV is just the average of the five bill values
EV = (1/5) * ($1 + $5 + $10 + $20 + $100)
EV = $27.20
Hope this helps,
