A box contains ten 1$ bills, five 2$ bills, three 5$ bills, one 10$ bill, and one 100$ bill. Find the expectation if one bill is selected

Question

Word problems

Answer 1

Since there are 20 bills in all, the probabilities of $1, $2, $5, $10, $100 are, respectively,

10/20, 5/20, 3/20, 1/20 & 1/20.  (These will be reduced to lowest terms when used below.)

 

Therefore the E(X), or weighted average, is 1/2($1) + 1/4($2) + 3/20($5) + 1/20($10) + 1/20($100)

[each term is the product of a probability and its monetary amount].

 

I leave the computing to you.