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

Answer:

Initial expected value = 7.3 $

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

Step-by-step explanation:

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

$\texttt{Probability of picking 20 dollar bill}=\frac{2}{10}=0.2\\\\\texttt{Probability of picking 10 dollar bill}=\frac{1}{10}=0.1\\\\\texttt{Probability of picking 5 dollar bill}=\frac{4}{10}=0.4\\\\\texttt{Probability of picking 1 dollar bill}=\frac{3}{10}=0.3$

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

$\texttt{Probability of picking 20 dollar bill}=\frac{3}{12}=0.25\\\\\texttt{Probability of picking 10 dollar bill}=\frac{2}{12}=0.167\\\\\texttt{Probability of picking 5 dollar bill}=\frac{4}{12}=0.333\\\\\texttt{Probability of picking 1 dollar bill}=\frac{3}{12}=0.25$

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

Answer 2

Answer:

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

Step-by-step explanation:

ANSWER FOR PLATO