You are playing a board game with a friend. She owns and has developed the tiles Green Gardens and Silver Sidewalks.

If you roll an 8, you will land on Green Gardens and owe her $1500. You will be able to pay, but you will not have money left afterward. If you roll a 9, you will land on the tile King's Taxes and have to pay $75. If you roll a 10, you will land on Silver Sidewalks and owe her $2000, which is more than you can pay—and lose the game. If you roll a 7 or less, you will not have to pay any money to anyone.

Your friend offers you insurance. Pay her $500 before you roll and even if you land on Green Gardens or Silver Sidewalks, you will not have to pay any additional money. However, if you roll a 7, you will have to pay her $1000.

Use probabilities to find expected values. Then compare the amount of money you should expect to pay out on average, under her insurance and by chance. Is her deal fair?