Answer: $ -1
Let x be the amount the player will gain. Since the player loses $-2 each time they roll a die, we will subtract -2 from the amount the player earns.
Getting a 1 = $5 -$2
Getting a 2: $1 - $2
Getting any value that is not 1 or 2: -$2
Now, the probability of getting a 1 in a die is 1/6, which is the same as getting a 2.
The probability of getting any value that is not 1 or 2 is 4/6 (3, 4, 5, 6)
[tex]\begin{gathered} x=\frac{4}{6}(-2)+\frac{1}{6}(5-2)+\frac{1}{6}(1-2) \\ x=-1 \end{gathered}[/tex]Therefore, the expected earning for the game is $ -1
