From the course: Introduction to Probabilistic Knowledge Graphs: AI-Driven Inference and Real-World Applications

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Conditional probability and Bayes' Theorem

Conditional probability and Bayes' Theorem

From the course: Introduction to Probabilistic Knowledge Graphs: AI-Driven Inference and Real-World Applications

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Conditional probability and Bayes' Theorem

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Imagine you glance outside and see rain. Instantly you think, hmm, I'm more likely to be late. That quick belief update is conditional probability in action. In this video, we'll unpack what conditional probability means, how independence simplifies it, and how Bayes' theorem turns belief updates into clear math. So conditional probability asks, what is the probability of event A given that event B has occurred? P of A given B equals P of A and B divided by P of B Assuming P of B is greater than 0 Intuitively, if we restrict attention to the world where B happened How often does A also happen within that world? Here's an example Suppose 5% of people are left-handed 10% have red hair and 0.005% are both Then, P of left-handed given red-haired equals 0.005 divided by 0.10, which equals 0.05. Among red-haired people, about 5% are left-handed. Now independence. Two events A and B are independent if knowing that B occurred doesn't change the probability of A. Formally, P of A and B equals…

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