https://www.khanacademy.org/math/class-12-tg/x6469e28db15923ec:probability/x6469e28db15923ec:independent-and-dependent-events-conditional-probability-multiplication-theorem-and-baye-s-theorem-part-2/v/reliability-of-a-test-intro-to-bayes-theorem 2025-06-01T14:50:00.385158177Z Reliability of a test - Intro to Bayes theorem This video provides an introduction to Bayes' Theorem by examining the reliability of a medical diagnostic test. We'll explore a scenario where a test isn't 100% accurate and a disease is rare. Using a tree diagram, we'll calculate the probability that a person who tests positive for the disease actually has it. This example provides an intuitive understanding of why Bayes' theorem is so important. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Reliability of a test - Intro to Bayes theorem This video provides an introduction to Bayes' Theorem by examining the reliability of a medical diagnostic test. We'll explore a scenario where a test isn't 100% accurate and a disease is rare. Using a tree diagram, we'll calculate the probability that a person who tests positive for the disease actually has it. This example provides an intuitive understanding of why Bayes' theorem is so important. https://cdn.kastatic.org/ka-youtube-converted/IIExxhML8Sg.mp4/IIExxhML8Sg.mp4 495 Bayes' theorem https://www.khanacademy.org/math/class-12-tg/x6469e28db15923ec:probability/x6469e28db15923ec:independent-and-dependent-events-conditional-probability-multiplication-theorem-and-baye-s-theorem-part-2/v/probability-of-picking-balls-from-bags 2025-06-01T14:50:00.385158177Z Probability of picking balls from bags 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. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Probability of picking balls from bags 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. https://cdn.kastatic.org/ka-youtube-converted/x0vhZidhy0U.mp4/x0vhZidhy0U.mp4 443 Bayes' theorem https://www.khanacademy.org/math/class-12-tg/x6469e28db15923ec:probability/x6469e28db15923ec:independent-and-dependent-events-conditional-probability-multiplication-theorem-and-baye-s-theorem-part-2/v/probability-of-manufacturing-defected-items 2025-06-01T14:50:00.385158177Z Probability of manufacturing defected items This video demonstrates how to apply Bayes' theorem to solve real-world problems related to manufacturing and quality control. We will work through scenarios where different machines or operators produce items at different rates and with different defect percentages. Given that a randomly selected item is defective, we will calculate the probability that it was produced by a specific machine or operator. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Probability of manufacturing defected items This video demonstrates how to apply Bayes' theorem to solve real-world problems related to manufacturing and quality control. We will work through scenarios where different machines or operators produce items at different rates and with different defect percentages. Given that a randomly selected item is defective, we will calculate the probability that it was produced by a specific machine or operator. https://cdn.kastatic.org/ka-youtube-converted/5Y4fTN3Eozo.mp4/5Y4fTN3Eozo.mp4 462 Bayes' theorem https://www.khanacademy.org/math/class-12-tg/x6469e28db15923ec:probability/x6469e28db15923ec:independent-and-dependent-events-conditional-probability-multiplication-theorem-and-baye-s-theorem-part-2/v/probability-of-telling-the-truth 2025-06-01T14:50:00.385158177Z Probability of telling the truth In this video, we explore the classic conditional probability problem involving a person who doesn't always tell the truth. We'll analyze a scenario where a person tosses a coin and reports the outcome, given that they speak the truth with a certain probability (e.g., 4 out of 5 times). Using a tree diagram and Bayes' theorem, we'll calculate the probability that the coin toss was actually heads, given that the person reported heads. A similar problem involving a die roll is also covered. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Probability of telling the truth In this video, we explore the classic conditional probability problem involving a person who doesn't always tell the truth. We'll analyze a scenario where a person tosses a coin and reports the outcome, given that they speak the truth with a certain probability (e.g., 4 out of 5 times). Using a tree diagram and Bayes' theorem, we'll calculate the probability that the coin toss was actually heads, given that the person reported heads. A similar problem involving a die roll is also covered. https://cdn.kastatic.org/ka-youtube-converted/1GOBIeLm-xo.mp4/1GOBIeLm-xo.mp4 268 Bayes' theorem https://www.khanacademy.org/math/class-12-tg/x6469e28db15923ec:probability/x6469e28db15923ec:independent-and-dependent-events-conditional-probability-multiplication-theorem-and-baye-s-theorem-part-2/v/finding-probability-using-binomial-theorem 2025-06-01T14:50:00.385158177Z Finding probability using binomial theorem In this video, we explore how to apply the binomial theorem to solve probability problems. We'll work through an example where we need to find the probability that at most 6 people in a random sample of 10 are right-handed, given that 90% of the population is right-handed. We'll define the parameters for a binomial distribution (n, p, q) and use the complement event (finding the probability of 7 or more right-handed people) to simplify the calculation and arrive at the final answer. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Finding probability using binomial theorem In this video, we explore how to apply the binomial theorem to solve probability problems. We'll work through an example where we need to find the probability that at most 6 people in a random sample of 10 are right-handed, given that 90% of the population is right-handed. We'll define the parameters for a binomial distribution (n, p, q) and use the complement event (finding the probability of 7 or more right-handed people) to simplify the calculation and arrive at the final answer. https://cdn.kastatic.org/ka-youtube-converted/dX4RyTAIGxM.mp4/dX4RyTAIGxM.mp4 353 Bayes' theorem https://www.khanacademy.org/math/class-12-tg/x6469e28db15923ec:probability/x6469e28db15923ec:independent-and-dependent-events-conditional-probability-multiplication-theorem-and-baye-s-theorem-part-2/e/theorem-of-total-probability 2025-05-05T08:14:25.350149109Z Theorem of total probability Find total probability of an event by summing all cases. srijan exercise https://www.khanacademy.org/math/class-12-tg/x6469e28db15923ec:probability/x6469e28db15923ec:independent-and-dependent-events-conditional-probability-multiplication-theorem-and-baye-s-theorem-part-2/e/bayes-theorem 2025-05-05T08:14:25.350149109Z Bayes' theorem questions on bayes theorem srijan exercise