In a standard die with 6 sides, each side is numbered with a value from 1 to 6.
All sides have the same probability of being rolled, therefore each number have a probability of 1/6.
Using the formula for the expected value, we have:
[tex]\begin{gathered} E=\sum_{i\mathop{=}1}^nx_ip_i\\ \\ E=(-3)\frac{1}{6}+(1)\frac{1}{6}+(-2)\frac{1}{6}+(5)\frac{1}{6}+0(\frac{1}{6})+(1)(\frac{1}{6})\\ \\ E=(-3+1-2+5+0+1)\frac{1}{6}\\ \\ E=2(\frac{1}{6})=\frac{2}{6}=\frac{1}{3} \end{gathered}[/tex]Since the expected value is positive, we can expect to win money.
