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Soup Servings

Explore how to solve the Soup Servings problem using dynamic programming techniques. Understand the probability calculations involving multiple random serving operations, and learn to optimize solutions through memoization and tabulation for efficient problem solving.

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 ...