Question: A carnival game offers a $100 cash prize for anyone who can break a balloon by throwing a dart at it. It costs $5 to play, and you are 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.

(i) Create a probability model for this carnival game [Hint: Give the model in the form of a probability distribution table].

(ii) Find the expected number of darts you will throw.

(iii) Find your expected winnings.