Question: Problem 3 Consider the gambler's ruin problem where the goal is to reach $5, and in each step, a coin will be flipped with a

Problem 3 Consider the gambler's ruin problem where the goal is to reach $5, and in each step, a coin will be flipped with a 60% chance of coming up heads (earn \$1) and 40% chance of coming up tails (lose $1 ), until the goal is reached or there is no money left. (a) Model this stochastic process as a Markov chain. Clearly define the state space and one-step transition probability matrix. (b) What is the chance of reaching the goal $5, if the gambler start with $1 ? (c) What is the least amount of money that the gambler should have at the start of this game in order to make sure that the chance of achieving the goal is higher than 70%

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