Question 624879
if a person rolls doubles when tossing two dice, the roller profits $95. If the game is fair, how much should the person pay to play the game?
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&#9861;&#9856;   &#9861;&#9857;   &#9861;&#9858;   &#9861;&#9859;   &#9861;&#9860;  <font color="red">&#9861;&#9861;</font>

The probability of wnning (rolling doubles) is 6 out of 36 or {{{6/36}}
which reduces to {{{1/6}}}. 
The probability of losing is 1-{{{1/6}}} = {{{5/6}}}.

Let $N be the price to pay to make the game fair:

Possible      Probability 
 Outomes      of outcome      Expectation
------------------------------------------
    x               p             xp
------------------------------------------
   $95             1/6            95/6  
   -$N             5/6           -5N/6
-------------------------------------------
                         &#8721;xp = {{{95/6-(5N)/6}}}

 To make the game fair we set that = 0

              &#8721;xp = {{{95/6-(5N)/6}}} = 0

                    {{{95/6-(5N)/6}}} = 0

Multiply through by 6

                    95 - 5N = 0
                        -5N = -95
                          N = 19

So he should pay $19 to play to make the game fair.

Edwin</pre>