Proving Bayes theorem [Hinglish] | Probability | Grade 12 | Math | Khan Academy скачать в хорошем качестве

Proving Bayes theorem [Hinglish] | Probability | Grade 12 | Math | Khan Academy

In this video, we provide a formal, step-by-step proof of Bayes' theorem. We begin by explaining the concept of a partition of a sample space. Then, we derive the crucial Theorem of Total Probability, which expresses the probability of an event A in terms of its conditional probabilities on these partitions. Finally, by substituting the Theorem of Total Probability into the basic definition of conditional probability, we arrive at the complete formula for Bayes' theorem. Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now! (https://www.khanacademy.org/math/ncer...) Timestamps: 00:00 Introduction: A formal proof of Bayes' theorem 00:30 The Theorem of Total Probability: Breaking down P(A) using partitions 01:00 Deriving the Theorem of Total Probability using Venn diagrams and the multiplication rule 03:25 Starting with the definition of conditional probability: P(Ei|A) 03:40 Substituting the Theorem of Total Probability into the denominator to get Bayes' theorem Khan Academy India is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We have videos and exercises that have been translated into multiple Indian languages, and 15 million people around the globe learn on Khan Academy every month. Support Us: https://india.khanacademy.org/donate Created by Ashish Gupta