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Soup Servings

Explore how to apply dynamic programming techniques to solve the Soup Servings problem, focusing on probability calculations when serving soup A and B until one is empty. Understand the problem constraints and implement an efficient solution approach involving memoization and state evaluation.

Statement

You begin with two types of soup, A and B, each containing n milliliters. During each turn, exactly one of the following four operations is selected uniformly at random (each with probability 0.250.25), independent of all prior turns:

  • Serve 100100 mL of soup A and 00 mL of soup B.

  • Serve ...