Bayes' theorem tells you how to update prior beliefs when new evidence arrives. Posterior = (likelihood × prior) / evidence.
A medical example
A rare disease affects 1% of people. A test is 99% accurate. If you test positive, what's the chance you have the disease? Bayes says: much lower than 99% — because the disease is rare. Base rates matter.
Modern AI
Spam filters, medical diagnosis tools, and Bayesian neural networks all use this framework. Rational learning from data is Bayes in action.
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