How to Solve Soup Servings Problem
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Soup Servings
You have two soups, A and B, each starting with n mL. On every turn, one of the following four serving operations is chosen at random, each with probability 0.25 independent of all previous turns: pou...
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Understanding the Soup Servings Problem
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Problem Statement
You have two soups, A and B, each starting with n mL. On every turn, one of the following four serving operations is chosen at random, each with probability 0.25 independent of all previous turns: pour 100 mL from type A and 0 mL from type B pour 75 mL from type A and 25 mL from type B pour 50 mL from type A and 50 mL from type B pour 25 mL from type A and 75 mL from type B Note: There is no operation that pours 0 mL from A and 100 mL from B. The amounts from A and B are poured simultaneously during the turn. If an operation asks you to pour more than you have left of a soup, pour all that remains of that soup. The process stops immediately after any turn in which one of the soups is used up. Return the probability that A is used up before B, plus half the probability that both soups are used up in the same turn. Answers within 10-5 of the actual answer will be accepted.
Soup Servings
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Examples
n = 500.62500If we perform either of the first two serving operations, soup A will become empty first. If we perform the third operation, A and B will become empty at the same time. If we perform the fourth operation, B will become empty first. So the total probability of A becoming empty first plus half the probability that A and B become empty at the same time, is 0.25 * (1 + 1 + 0.5 + 0) = 0.625.
n = 1000.71875If we perform the first serving operation, soup A will become empty first. If we perform the second serving operations, A will become empty on performing operation [1, 2, 3], and both A and B become empty on performing operation 4. If we perform the third operation, A will become empty on performing operation [1, 2], and both A and B become empty on performing operation 3. If we perform the fourth operation, A will become empty on performing operation 1, and both A and B become empty on performing operation 2. So the total probability of A becoming empty first plus half the probability that A and B become empt
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