Martingale strategies in gambling. A player plays the following game at a casino: The player puts in an amount X in money. A fair coin is tossed. If the coin shows heads, the player receives 2X in return; otherwise he gets nothing- Karen goes to the casino with 1000$ and plays the following strategy: In her first game, she puts in 1$. If she wins, she finishes playing and takes her profit home. If she looses a game, she will play another game and put in twice as much money as she did in the previous game. If she wins, she will finish playing and take her profits home. She will keep going with that strategy, until she either wins a game or runs out of money. (a) Create a table for n = 1, 2,..., 10 which lists: (a) The amount of money she puts in in game n; (b) the sum of the amount of money she has put in in all games up to this game n; and (c) her overall profit if the game n is the first game she wins. (b) What is the likelihood of her loosing 8 games in a row? (c) How many games can she loose in a row before she cannot afford to continue with her strategy of doubling her bet? (d) Given the low likelihood of loosing, is this a smart strategy for Karen to pursue