Respuesta :
ANSWER:
The expected profit is $ -11.48 (That is a loss, not profit)
STEP-BY-STEP 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:
[tex]\begin{gathered} \text{Probability of winning } \\ \frac{1}{250} \\ \text{Probability of losing } \\ \frac{249}{250} \end{gathered}[/tex]Now we must calculate the gain or loss of winning and thethe gain or loss of losing:
[tex]\begin{gathered} \text{ Gain or loss of winning} \\ 380-13=367 \\ \text{ Gain or loss of losing} \\ -13 \end{gathered}[/tex]Now we calculate the expected value as follows:
[tex]\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=\frac{1}{250}\cdot367+\frac{249}{250}\cdot-13 \\ E=\frac{367}{250}-\frac{3237}{250} \\ E=\frac{367-3237}{250} \\ E=\frac{-2870}{250} \\ E=-11.48 \end{gathered}[/tex]