A game is played by flipping a fair coin 4 times. If you obtain 3 or 4 tails, you win $500. If you obtain 2 tails, you lose $400. Otherwise you don't win or lose anything.

This question has 3 parts:

(a)Find an ideal data set for the payoffs of this game.

(b)Explain briefly what it means for your answer to (a) to be an ideal data set.

(c)Use the ideal data set from (a) to find how much you make or lose per play of the game, on average, in the long run.