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A 99% accurate medical test says you're positive — but there's only a 9% chance you're actually sick. How is that possible? This is Bayes' theorem, and it's the same equation powering every AI system that reasons under uncertainty. In Episode 3 of The Math Behind AI, we build Bayes' theorem from scratch — starting with what probability really means, deriving the formula step by step, and revealing why even highly accurate tests can be dangerously misleading. Then we use it to build a real AI spam classifier, watch prior beliefs morph into sharp posteriors, and discover that every neural network trained with weight decay is secretly doing Bayesian inference. 📑 CHAPTERS 0:00 The 99% Paradox — Hook 0:25 What Is Probability? 1:17 Conditional Probability 2:13 Deriving Bayes' Theorem 3:11 Medical Test Deep Dive 4:10 Naive Bayes Spam Filter 5:17 Updating Beliefs — Prior to Posterior 6:13 Bayes in Machine Learning 7:23 Recap & Episode 4 Preview 📌 Series Playlist: • The Math Behind AI — From Vectors to Trans... 📌 Previous Episode: EP2 — Gradient Descent: How AI Learns 📌 Next Episode: EP4 — Backpropagation (Coming Soon) #TheMathBehindAI #BayesTheorem #MachineLearning