A bin consists of 4 \$10 bills, 3 \$20 bills and 1 \$100 bill. You select 7 bills out of this bin uniformly at random without replacement. Find the expected value of the sum of all the bills you select.
What would be the best way to approach this question? Can I use linearity of expectation? Does exchangeability have anything to do with this question?
Thanks :)
The total value of bills is $4\times 10+3\times 20+1\times 100=200$. The value $X$ of the 7 bills you draw is $X=200-Y$ where $Y$ is the value of the last remaining bill. Computing $\mathbb{E} Y$ is easy. Now you can work out $\mathbb{E}X$.