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 ->  Probability-and-statistics -> 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?       Log On


   

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) About Me  (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