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 first step to doing probability is to count the total number of bills in the box, which in this case is 9+8+2+4 which is 23. Since there are 9 $1 bills, it is 9 out of 23 which could also be written as 9/23 and there's you're answer.

Answer 2

the word ONE is not representative of the ONE dollar bills in this case, it means a "single" bill is selected.

Answer 3

But yah Riti has the right idea.

So the total number of bills is 23.

The expected value of the $1 bills we can represent this way, as Riti explained,\[\large $1\left(\frac{9}{23}\right)\]We'll add to that the value of each other bill as well. This will give us the value we should expect to gain from one bill selection.\[\large $1\left(\frac{9}{23}\right)+$5\left(\frac{8}{23}\right)+$10\left(\frac{2}{23}\right)+$20\left(\frac{4}{23}\right)\]

Which ends up giving us an expectation of around $4.74 on a single bill selection.