In a die game , a player pays a stake of $\$1$ for each throw of a die. She receives $\$5$, if the die shows a 3, $\$2$ if the die shows 1 or 6 and nothing otherwise. What is the player expected profit per throw over a long series of throws?

Question

$\begin{array}{1 1} \$0.50 \\ \$ 1 \\ \$2 \\ \$4 \end{array}$