You need to show your work (formula setup, calculations, etc.) and state any properties or rules you need to solve the problems.

1) A carnival game offers a $100 cash prize for anyone who can burst the balloon by throwing a dart. It costs $5 to play, and you're willing to spend up to $20 trying to win. You estimate that you have about a 10% chance of hitting the balloon on any throw. A winning is the profit you make taking into account the cash prize and the amount paid to play the game.

(a) Make a probability model for this carnival game.

(b) Find the expected number of darts you'll throw.

(c) Find your expected winnings.