Answer:
The expected value can be calculated as:
Es = x₁*p₁ + x₂*p2 + .....
where xₙ is the event (the amount of money that you win or lose, and pₙ is the probability for the event)
for example, in a 10 side dice, the probability of obtaining a specific number is 1/10.
we have a d10 i guess (a dice with 10 sides, 1 to 10)
if you roll from 1 to 7, nothing happens.
If you roll an 8, you lose $1500
if you roll a 9, you lose $75
if you roll a 10, you lose $2000 (and the game)
the expected value is,
Es = 1/10*(7*0 - 1*$1500 - 1*$75 - 1*$2000) = -$357
in the second case, you start paying $500.
if you roll a 7, you must pay $1000, if else, nothing happens.
Then the expected value is
Es = -$500 - 1/10*(-1*$1000 + 9*$0) = -$600
So the expected value is smaller in this case, so the deal is not fair
