SOLUTION: In a gambling game a man is paid $3 if he draws a jack or queen and $5 if he draws a king or ace from an ordinary deck of 52 playing cards. If he draws any other card, he looses. H

Algebra ->  Probability-and-statistics -> SOLUTION: In a gambling game a man is paid $3 if he draws a jack or queen and $5 if he draws a king or ace from an ordinary deck of 52 playing cards. If he draws any other card, he looses. H      Log On


   



Question 507184: In a gambling game a man is paid $3 if he draws a jack or queen and $5 if he draws a king or ace from an ordinary deck of 52 playing cards. If he draws any other card, he looses. How much should he pay to play if the game is fair?
Answer by Edwin McCravy(20063) About Me  (Show Source):
You can put this solution on YOUR website!
In a gambling game a man is paid $3 if he draws a jack or queen and $5 if he draws a king or ace from an ordinary deck of 52 playing cards. If he draws any other card, he looses. How much should he pay to play if the game is fair?
Suppose he pays x dollars to play:

           X          P(X)      E(X)=X*P(X)
Draw    Winnings   Probability   Expection  
  J       3-x         1%2F13          expr%281%2F13%29%283-x%29 
  Q       3-x         1%2F13          expr%281%2F13%29%283-x%29
  K       5-x         1%2F13          expr%281%2F13%29%285-x%29
  A       5-x         1%2F13          expr%281%2F13%29%285-x%29
other      -x         9%2F13          expr%289%2F13%29%28-x%29



Set that = 0



Multiply through by 13

%283-x%29%2B%283-x%29%2B%285-x%29%2B%285-x%29-9x=0

3-x%2B3-x%2B5-x%2B5-x-9x=0

16-13x=0

-13x=-16

x=16%2F13=%22%241.23%221%2F13


Edwin