Question

n a bag there are two $20 bills, one $10 bill, four $5 bills, and three $1 bills. If Frank picks one bill from the bag, the expected value of the bill he chooses is ____$. If one more $20 bill and one more $10 bill are added to the bag, the expected value will change to _____$.

Answer 1

$7.30 for the first one and $8.58 for the second one

Explanation:

ANSWER FOR PLATO

Answer 2

Initial expected value = 7.3 $

If one more $20 bill and one more $10 bill are added to the bag expected value = 8.57 $

Explanation:

a) Total number of bills = 2 + 1 + 4 + 3 = 10

`\texttt{Probability of picking 20 dollar bill}=(2)/(10)=0.2\\\\\texttt{Probability of picking 10 dollar bill}=(1)/(10)=0.1\\\\\texttt{Probability of picking 5 dollar bill}=(4)/(10)=0.4\\\\\texttt{Probability of picking 1 dollar bill}=(3)/(10)=0.3`

Expected value = 20 x 0.2 + 10 x 0.1 + 5 x 0.4 + 1 x 0.3 = 7.3$

b)If one more $20 bill and one more $10 bill are added to the bag

Total number of bills = 3 + 2+ 4 + 3 = 12

`\texttt{Probability of picking 20 dollar bill}=(3)/(12)=0.25\\\\\texttt{Probability of picking 10 dollar bill}=(2)/(12)=0.167\\\\\texttt{Probability of picking 5 dollar bill}=(4)/(12)=0.333\\\\\texttt{Probability of picking 1 dollar bill}=(3)/(12)=0.25`

Expected value = 20 x 0.25 + 10 x 0.167 + 5 x 0.333 + 1 x 0.25 = 8.57$