SOLUTION: A Barrel has 20 $1, 10 $2, 5 $5, 3 $10, 1 $20 and 1 $100 dollar bill. What should we charge to make the game profitable for those in charge of the game?

Algebra.Com
Question 891260: A Barrel has 20 $1, 10 $2, 5 $5, 3 $10, 1 $20 and 1 $100 dollar bill. What should we charge to make the game profitable for those in charge of the game?
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
I will assume that a player gets to reach in the barrel and blindly 
select 1 bill that he is allowed to keep.

There are 20+10+5+3+1+1 = 40 bills

Value    Probability    Expectation
 of          of         = Value × 
Bill      drawing       Probability   
--------------------------------------------  
  $1       20/40 = 1/2   $1×(1/2)  =   $0.50             
  $2       10/40 = 1/4   $2×(1/4)  =   $0.50
  $5        5/40 = 1/8   $5×(1/8)  =   $0.625 
 $10        3/40        $10×(3/40) =   $0.75
 $20        1/40        $20×(1/40) =   $0.50
$100        1/40       $100×(1/40) =   $2.50
--------------------------------------------
Totals     40/40 = 1                   $5.375

If a player plays the game many times, she/he will average
walking away with $5.375 each time.  So to make the game 
profitable to those in charge, they should charge more than
$5.375 to play.  [For instance if they charge $10 to play, 
they will average profiting $10.00 - $5.375 or $4.625 each 
time someone plays.]

Edwin
RELATED QUESTIONS

a game is played by selecting one bill at random from a bag that contains ten $1 bills,... (answered by Mathtut)
A game is played by selecting one bill at random from a bag that contains eight $1 bills, (answered by solver91311)
I need help with the following problem: in her wallet, anne has 14 bills, seven are $1 (answered by stanbon)
Alex has won a radio contest that allows him to draw three bills that he can keep from a... (answered by Edwin McCravy)
A box contains one each of $1, $5, $10, $20, and $100 bills. It costs $16 to reach in and (answered by ikleyn)
Tom has a $20 bill, a $10 bill, a $5 bill and a $1 bill. List the total costs possible... (answered by AnlytcPhil)
a game is to be played where there is a box with 3-$100 bill, 5-$20 bills, 2-$5.00 bills... (answered by stanbon)
Tom has a $20 bill, a $10 bill, a $5 bill, and $1 bill. List the total costs possible for (answered by KMST)
Grace has 20% of $100. Chulsoo has 10% of Grace's. What percent of $100 does Chulsoo... (answered by richwmiller)