Session-01

Why Every AI Decision is a Probability Problem

What does an LLM actually do when it generates text? It searches for the most likely next token — and probability is what makes that search principled. In this segment, Ajay frames the entire course through three high-stakes decisions: routing load to servers, ranking items in a recommender system, and measuring whether Algorithm A beats Algorithm B in an A/B test. Can you express $P(\text{click} | \text{algo}_1)$ vs $P(\text{click} | \text{algo}_2)$ before we have formal definitions?

graph LR LLM["LLM next-token"] --> PATH["Path search over tokens"] PATH --> PA["P(path A)"] PATH --> PB["P(path B)"] LOAD["Load balancer"] --> S1["Server 1"] LOAD --> S2["Server 2"] AB["A/B test"] --> C1["P(click|algo1)"] AB --> C2["P(click|algo2)"]

You have seen that real product decisions — load balancing, ranking, experimentation — reduce to comparing probabilities. Before we can compare $P(A)$ and $P(B)$, we need a precise language for probability itself. The next segment builds that language from scratch using the simplest experiment you know: flipping a coin and rolling a die.

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Sample Spaces

Conditional Probability: How New Information Changes Everything

From Click-Through Rates to the Law of Total Probability