Answer: The expected value is -$0.33
Step-by-step explanation: The expected value is calculated as:
E = ∑pₙxₙ
where xₙ is a given event (in this case winning 8$ or losing 2$) and pₙ is the probability for the event.
So in this you only win with one result in the dice, so the probability of winning is 1/6, and the probability of losing must be 5/6.
Then the expected value is:
E = 1/6*$8 - 5/6*$2 = $-0.33
Where I used the profit of $8 instead of $10, because you must pay $2 for play, and you win $10, the profit is ($10 - $2) = $8