Stanley Statistics, an infamous statistician, wants you to enter a friendly wager with him. For \(\$ 1,000\), he will let you play the following game. He will continue to toss a fair coin until the first head appears. Letting \(x\) represent the number of times the coin was tossed to get the first heads, Stanley will then pay you \(\$ 2^{x}\).

(a) Define a probability space for the experiment of observing how many times a coin must be tossed in order to observe the first heads.

(b) What is the expected payment that you will receive if you play the game?

(c) Do you want to play the game? Why or why not?