Question 1161335
<font face="Times New Roman" size="+2">


1 of 13 diamonds is an Ace, 3 of 13 diamonds are face cards, the other 9 cards are 2 through 10.


<pre>
Card    X      P(X)   
Ace   -20      1/13
Face   10      3/13
2-10    2      9/13
</pre>

The expected value is the sum of X times P(x) for each of the three possible outcomes, Ace, Face, or 2-10.  A perfectly fair game has an expected value of zero.  A positive expected value favors the player and a negative expected value favors the owner of the game.  In this case, it is not possible given that you need to round the charge to play the game to the nearest cent to charge an amount that makes the game perfectly fair.  You will find, when you do the arithmetic, that charging $2.15 to play very slightly favors the player and $2.16 very slightly favors the owner of the game.
								
								
John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
<img src="http://c0rk.blogs.com/gr0undzer0/darwin-fish.jpg">
*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \  
								
{{n}\choose{r}}
</font>