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Soup Servings

Explore dynamic programming techniques to solve the Soup Servings problem, where you calculate the probability that soup A becomes empty before soup B under random serving conditions. Learn how to model the process, handle probabilistic states, and use memoization for efficient computation.

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 ...