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In this video, we solve several classic probability problems involving drawing balls from different bags, which are perfect applications of Bayes' theorem and the law of total probability. We'll tackle scenarios where a bag is chosen at random before a ball is drawn, and then use the outcome of the draw to determine the probability it came from a specific bag. We'll also look at a problem where the composition of the urn changes based on the first draw. Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now! (https://www.khanacademy.org/math/ncer...) Timestamps: 00:00 Problem 1: Ball drawn from one of two bags is red. Find P(it was from Bag II). 03:00 Problem 2: Ball drawn, noted, returned with 2 more of the same color. Find P(second ball is red). 05:00 Problem 3: Ball drawn from one of two bags is red. Find P(it was from the first bag) 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