Probability and Bayes' theorem

Probability is the language of uncertainty, and it runs through ML. A spam classifier outputs P(spam | email), the chance an email is spam given what it says, not a certainty. Learn joint, marginal and conditional probability, independence, and Bayes' theorem: P(A | B) = P(B | A) × P(A) / P(B).

Bayes explains the base rate trap. Say a disease affects 1% of people and a test is 99% accurate. A positive result then means only about a 50% chance of having it.

Why? The false positives from the 99% of healthy people roughly equal the true positives from the sick 1%. The same logic explains why a fraud model that catches most fraud (high recall) can still flag mostly innocent transactions.

Work these out with counts from a table of 10,000 people; it is far more intuitive than the formula alone.