Question

A box contains one each of $1, $5, $10, $20, and $100 bills. you reach in and withdraw one bill. what is the expected value?

Answer 1

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,