Question

A game is played using one die. If the die is rolled and shows 1​, the player wins $ 10. If the die shows any number other than 1​, the player wins nothing. a.If there is a charge of $ 2 to play the​ game, what is the​ game's expected​ value?

Answer 1

For each roll you start with paying 2 dollars and you only with 10 dollars one out of 6 rolls (on average).

So the cost for one play is 2 dollars and your win is 10/6.
Value is -2+10/6=-1/3 dollars

So you lose 1/3 dollars on average with each game.