Question

Sandi randomly selects a single bill from an envelope containing 8 ones, 5 fives, 4 tens, and 3 twenties. Whatis the expected value of the money she selects?expected value =

Answer 1

the formula to get the expected value is

`E(x)=\sum ^n_(i\mathop=1)x_if(x_i)`

So, first we calculate teh probabilities. We have 20 bills in total. so we divide the quantity of bills of each value by the total:

we have 8 ones: 8/20= 2/5

5 fives: 5/20=1/4

4 tens: 4/20= 1/5

3 twenties = 3/20

now, we multiply each value with te probabilitiy of picking it and add all

`E=\text{ 1}\cdot(2)/(5)+5\cdot(1)/(4)+10\cdot(1)/(5)+3\cdot(3)/(20)=\text{ 4.1}`

the expected value is 4.1