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Quantitative foundations · Vectors and uncertainty

Probability, sampling, and conditional reasoning

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Probability describes uncertainty under a model of possible outcomes. A conditional probability changes the question by restricting what is already known. The probability that a flagged ticket is urgent differs from the probability that an urgent ticket is flagged.

A sample is only informative to the extent that it represents the situation you care about. Evaluating only easy tickets can produce a high score that fails in production. Repeated or near-duplicate examples can also create a false sense of sample size.

Write the population, sampling method, and excluded cases next to every result. Small samples can be useful for finding failures but support limited claims about general performance.

Exercise: create a table of flagged/unflagged and urgent/non-urgent tickets. Calculate both conditional probabilities and explain why they differ.

Check: you can state the denominator for each metric and explain what your sample does not establish.

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Probability, sampling, and conditional reasoning | AI Engineer | Android Engineers