Answer:
[tex](-28/13)[/tex], which is approximately [tex](-2.15)[/tex].
Step-by-step explanation:
The average return is the average of all possible values, weighted according to the probability of each value. In the game in this question:
- A value of [tex]20[/tex] if a king is drawn, with a probability of [tex](1/13)[/tex] (one in each suit of [tex]13[/tex] cards), and
- A value of [tex](-4)[/tex] if any other card is drawn, with a probability of [tex](12/13)[/tex].
The average of the values, averaged by probability, would be:
[tex]\begin{aligned}& \frac{1}{13} \times 20 + \frac{12}{13} \times (-4) \\ =\; & -\frac{28}{13} \\ \approx\; & -2.15\end{aligned}[/tex].
In other words, the average return of this game would be approximately [tex](-2.15)[/tex], meaning that the player would lose on average.
