ANSWER:
The expected profit is $ -11.48 (That is a loss, not profit)
Explanation:
The first thing is to calculate the probability of winning and the probability of losing, knowing that only 1 in 250 people would win it, therefore:

Now we must calculate the gain or loss of winning and thethe gain or loss of losing:

Now we calculate the expected value as follows:
![\begin{gathered} E=\text{Probability of winning }\cdot\text{ Gain or loss of winning}+\text{Probability of losing }\cdot\text{Gain or loss of losing} \\ E=(1)/(250)\cdot367+(249)/(250)\cdot-13 \\ E=(367)/(250)-(3237)/(250) \\ E=(367-3237)/(250) \\ E=(-2870)/(250) \\ E=-11.48 \end{gathered}]()