Find the expected payback for a game in which you bet 2000.
Solution:-
Let x, the random variable, represent the possible amounts of payback, where payback is the amount won less the cost.
The payback for winning is 20 = 1980.
The payback for losing is 20 =
1980
![Rendered by QuickLaTeX.com - 20</td> </tr> <tr> <td width="145">P(x)</td> <td width="145">(probability)</td> <td width="145">0.0100</td> <td width="145">0.9900</td> </tr> </tbody> </table> The expected payback is calculated using the expected values formula, E(x) = x<sub>1</sub>p<sub>1</sub> + …..+x<sub>n</sub>p<sub>n</sub>. Substitute the values of x and p into the expected value formula and calculate. E(x) = (](https://mymathangels.com/wp-content/ql-cache/quicklatex.com-ddf73e44438dcfad66ad4efe0b04c655_l3.png)
![Rendered by QuickLaTeX.com -20)*(0.9900) =](https://mymathangels.com/wp-content/ql-cache/quicklatex.com-c539b26e9d6876b490043525a454af01_l3.png)
Therefore , the expected payback is $0.00.
Note that a game with an expected value of 0 is called a fair game.