Answer: $7.70
Step-by-step explanation:
Given : A box contains eighteen $1 bills, ten $5 bills, eight $10 bills, three $20 bills, and one $100 bill.
Total bills = [tex]18+10+8+3+1=40[/tex]
We know that probability of any event =[tex]\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}[/tex]
i.e. the probability of getting $1 bills =[tex]P(E_1)=\dfrac{18}{40}=0.45[/tex]
Probability of getting $10 bills =[tex]P(E_2)=\dfrac{10}{40}=0.25[/tex]
Probability of getting $5 bills =[tex]P(E_3)=\dfrac{8}{40}=0.2[/tex]
Probability of getting $20 bills =[tex]P(E_4)=\dfrac{3}{40}=0.075[/tex]
Probability of getting $100 bills =[tex]P(E_5)=\dfrac{1}{40}=0.025[/tex]
[tex]\text{Expected value =}1\times P(E_1)+5\times P(E_2)+10\times P(E_3)+20\times P(E_4)+100\times P(E_5)\\\\=1\times 0.45+5\times 0.25+10\times0.2+20\times 0.075+100\times 0.025\\\\=7.7[/tex]
Hence, the expected value of your draw= $7.70