Question: USE DYNAMIC PROGRAMMING NOT JUST PROBABILITY FOR THIS QUESTION: Consider a dynamic programming problem, with three stages: n = 1, 2, 3. At each stage

USE DYNAMIC PROGRAMMING NOT JUST PROBABILITY FOR THIS QUESTION:

Consider a dynamic programming problem, with three stages: n = 1, 2, 3. At each stage your state Sn is the total number of chips you have. Let S1 = 2 (the number of chips at the beginning stage). At each stage you can bet as many chips as you wish, up to the total number of chips you have at that time. You must bet at least one chip each time. You win or lose as many chips as you bet. The probability of winning each bet is 0.45. By using dynamic programming, find the maximum probability of having at least 3 chips at the conclusion of Stage 3. At the end of your work, explicitly say what that maximum probability is. Also, give all possible optimum paths, in terms of how many chips to bet each time.

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