You play a game at a casino that involves rolling a fair die

You play a game at a casino that involves rolling a fair die. If you roll a 1, the house pays you $25. If you roll a 2, the house pays you $5. If you roll a 3, you win nothing. If you roll a 4 or 5, you must pay the house $10. If you roll a 6, you must pay the house $15. What is the expected value of the game? (Hint: the expected value aka average return, is the sum of the individual probabilities of each roll multiplied by the corresponding payback.)

Solution

It is a fair die so probability of each number is equal and there are 6 numbers so probability of each number coming up on a roll of die is 1/6

So to calculate expected value we take the money payed by house as positive and money paid to the house as negative

So expected value is

1/6(25+5+0-10-10-15)=-5/6

So expected value is negative is $5/6 is expected to be paid to the house