Answer:
-$6.72
Explanation:
The cost of the ticket = $10
Let X be the possible profit on the ticket.
The probability distribution for X is given below.
Thus, the expected value for your profit is calculated below:
![\begin{gathered} E(X)=\sum xP(x) \\ =\left(1000*(1)/(800)\right)+\left(300*(4)/(800)\right)+\left(30*(14)/(800)\right) \\ =3.28 \end{gathered}](https://img.qammunity.org/qa-images/2023/formulas/mathematics/college/3xd68ankinf4z0ulekfx.png)
Subtract from 10:
![3.28-10=-\$6.72](https://img.qammunity.org/qa-images/2023/formulas/mathematics/college/4juinyv2k5sfck9m3pzw.png)
The expected value for your profit is -$6.72.
Note: This means that if you play the game, you expect to make a loss of $6.72 (rounded to the nearest cent).