Question

A box contains nine $1 bills, eight $5 bills, two $10 bills, and four $20 bills. What is the expectation if one bill is selected?

Answer 1

The expectation is probably a $1 bill because there is more of them.
There is a total of (9 + 8 + 2 + 4) = 23 bills.
The chance of getting a $1 is 9/23, the chance of getting a $5 bill is 8/23, the chance of getting a $10 is 2/23, and the chance of getting a $20 is 4/23.

Answer 2

The expectation (or expected value) is the sum of the probabilities multiplied by the payoffs. So \[\frac{9}{23} * $1 + \frac{8}{23}*$5 + ...\]

Answer 3

1/24