Probability basics for AI

Probability measures how strongly we should expect an outcome, from 0 (impossible) to 1 (certain). AI uses probabilities for classifications, sampling, and uncertainty.

Models often output scores that *look* like probabilities. Knowing the basics helps you ask whether those scores are calibrated—and pairs with Course 06 uncertainty and Course 29 medical overtrust.

• Events: “email is spam”
• Conditional: “spam *given* it mentions gift cards”
• Bayes intuition: update beliefs when evidence arrives (see Course 06 chapter)

Independence matters: assuming features are independent when they are not can mislead naive models.

A 10% chance of rain does not mean light rain—it means rain happens in about 1 of 10 similar days.

Write one prior belief and one piece of evidence that should raise or lower it.

⚠️ Myth: Softmax outputs are always true probabilities of the real world.

✓ Reality: They are normalized scores; calibration is separate.

⚠️ Myth: Rare events can be ignored if the average case looks fine.

✓ Reality: Safety-critical tails matter.

• Elements of AI: https://www.elementsofai.com/ ↗
• Course 06 uncertainty-and-bayesian-thinking
• Khan Academy probability (verify): https://www.khanacademy.org/math/statistics-probability ↗