Please solve this question. thank you.

Question 6. [Marks:10] a) Distinguish between deterministic and probabilistic dynamic programming. [2] b) An enterprising young statistician believes that she has developed a system for [8] winning a popular Las Vegas game. Her colleagues do not believe that her system works, so they have made a large bet with her that if she starts with three chips, she will not have at least four chips after three plays of the game. Each play of the game involves betting any desired number of available chips and then either winning or losing this number of chips. She can stop the play if four or more chips have been acquired at any of the three plays. The probability of losing a given play of the game is 0.3 as per the statistician's calculation. The decision at each play should take into account the results of earlier plays. Determine the optimal policy of how many chips to bet (if any) at each of the three plays of the game to maximize the winning probability