value of the money you win when you stop? Can you earn $100 by playing the game in some way?Please give a complete answer and show your work clearly.

Suppose you’re playing a game: You put out x dollars. A coin is flipped. If heads, you get 2x dollars. If tails, you get 0 dollars.: Is this a fair game?Now suppose you can play the game infinitely many times. You put out $1. If you win, you stop. If you lose, you put out $2. If you win, you stop. If you lose, you put out $4 (double the previous amount). You continue the same way until you win the first time.: What is the probability that you stop? What is the expected value of the money you win when you stop? Can you earn $100 by playing the game in some way?Please give a complete answer and show your work clearly.