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Question 2. [8 Marks] A gambler has $20 and needs to increase it to $100 in a hurry. He can play;r a game with the following rules: a fair coin is tossed; if a player bets correctlyIr on heads or tails, he wins a sum equal to his stake, and his stake is returned; otherwise, he loses his stake. The gambler decides to use the following bold strategy: if he has $50 or less, he stakes all his money on the nest coin toss; otherwise, he stakes just enough to increase his capital, if he wins, to $100. Let X0 = 20 and let Xn be the gamble's capital after it tosses of the coin. (a) What is the appropriate sample space. given the gambler's strategy. (h) Prove that the gambler will achieve his aim with probabilin 1 f 5. (c) Find the expected total number of tosses until the gambler either achieves his aim or loses his capital