SOLUTION: a case game consist of one card out of 52. If you get a king or a queen you win 5 dollars. If you select any hearts you win 2 dollars. How much should you pay to keep the game fair

Question 274643: a case game consist of one card out of 52. If you get a king or a queen you win 5 dollars. If you select any hearts you win 2 dollars. How much should you pay to keep the game fair?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
a case game consist of one card out of 52. If you get a king or a queen you win 5 dollars. If you select any hearts you win 2 dollars. How much should you pay to keep the game fair?
------------------------------
Let the cost to play be "x" dollars.
-------------------------------
Random gain values: 5-x ; 2-x ; -x
Probabilities::::: 8/52 ; 13/52 ; 31/52
---------------------------------------------
Note: If the game is fair expected gain should be zero.
---------------------------------------------
Equation:
E(x) = (8/52)(5-x) + (13/52)(2-x) + (31/52)x = 0
----------
Multiply thru by 52 to get:
[40 - 8x + 26 - 13x + 31x) = 0
10x - 66 = 0
x = $6.60 (amount you should pay to play the game)
=====================================
Cheers,
Stan H.
RELATED QUESTIONS
In this carnival game project(that we have to do for math end of the year project), round (answered by stanbon)

5.) A card game goes like this: You draw a card from a 52-card deck. If it is a face card (answered by stanbon)

A card game goes like this: You draw a card from a 52-card deck. If it is a face card... (answered by solver91311)

A card game goes like this: You draw a card from a 52-card deck. If it is a face card... (answered by stanbon)

A carnival game is played as follows: You pay $2 to draw a card from an ordinary deck of (answered by stanbon)

A card game goes like this: You draw a card from a 52-card deck. If it is a face card... (answered by ikleyn)

We had to make a probability game in Gr 12 Data Management. We now have to find out the... (answered by venugopalramana)

You play a game based on drawing a single card from a standard deck. You win$6 dollars if (answered by lynnlo)

You draw a card from a standard deck of 52 cards. Find the P(King or a... (answered by ikleyn)