Carnival 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 (they keep your $5, even if you win the $100), and you’re willing to...

Carnival 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 (they keep your $5, even if you win the $100), 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) Create a probability model for this carnival game.

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

 c) Find your expected winnings.