https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:prob-comb/x9e81a4f98389efdf:compound-probability-of-ind-events-using-mult-rule/v/introduction-to-dependent-probability 2021-07-01T17:39:50Z Dependent probability introduction Let's get you started with a great explanation of dependent probability using a scenario involving a casino game. Sal Khan video https://cdn.kastatic.org/googleusercontent/XZe8ECJLHJW98AgXE5te2kLXlmb1nZx9lAGUT9wWpOEKBoogYPeLIqLDnwkrWnDZ-rydfl-Pf5PuZZgb4ectsZiF Dependent probability introduction Let's get you started with a great explanation of dependent probability using a scenario involving a casino game. https://cdn.kastatic.org/ka-youtube-converted/VjLEoo3hIoM.mp4/VjLEoo3hIoM.mp4 398 Solving probability using the laws of probability and Bayes' rule. https://www.khanacademy.org/math/statistics-probability/probability-library/multiplication-rule-dependent/v/analyzing-dependent-probability 2021-03-12T17:07:31Z Dependent probability Sal finds dependent probabilities like P(A | B) using an example rolling dice. Sal Khan video https://cdn.kastatic.org/googleusercontent/PurKXVlt4QA1_iE3JWMdCpqp69zAiuT59msnC8LZiOqZ__vXsFbx7Pf2ZN5mnPYpUpjBrOH03I0VzMs-p-CE9Vg Dependent probability Sal finds dependent probabilities like P(A | B) using an example rolling dice. https://cdn.kastatic.org/ka-youtube-converted/8iKsY8C5VW8.mp4/8iKsY8C5VW8.mp4 570 Solving probability using the laws of probability and Bayes' rule. https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:prob-comb/x9e81a4f98389efdf:compound-probability-of-ind-events-using-mult-rule/v/general-multiplication-rule-example-dependent 2022-10-07T00:22:18.752150461Z General multiplication rule example: dependent events We can use the general multiplication rule to find the probability that two events both occur when the events are not independent. Sal Khan video https://cdn.kastatic.org/ka_thumbnails_cache/038c6b23-2d48-4ceb-960e-5f4d99175cf0_1280_720_base.png General multiplication rule example: dependent events We can use the general multiplication rule to find the probability that two events both occur when the events are not independent. https://cdn.kastatic.org/ka-youtube-converted/iyQNk090FGM.mp4/iyQNk090FGM.mp4 159 Solving probability using the laws of probability and Bayes' rule. https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:prob-comb/x9e81a4f98389efdf:compound-probability-of-ind-events-using-mult-rule/v/interpreting-general-multiplication-rule 2022-10-07T00:22:18.752150461Z Interpreting general multiplication rule We can express the probability that two events both occur symbolically using the general multiplication rule, and we can interpret probability statements that are expressed symbolically. Sal Khan video https://cdn.kastatic.org/ka_thumbnails_cache/12debcfa-c173-42b7-bffd-810bcfde0794_1280_720_base.png Interpreting general multiplication rule We can express the probability that two events both occur symbolically using the general multiplication rule, and we can interpret probability statements that are expressed symbolically. https://cdn.kastatic.org/ka-youtube-converted/yTJawPRzCzI.mp4/yTJawPRzCzI.mp4 291 Solving probability using the laws of probability and Bayes' rule. https://www.khanacademy.org/math/ka-math-class-12/x6f66cbee9a2f805b:probability-ncert-new/x6f66cbee9a2f805b:applications-of-bayes-theorem/v/using-bayes-theorem-for-dice-coins-and-cards 2025-06-01T14:50:00.385158177Z Using Bayes theorem for Dice, coins, and cards In this video, we solve a series of complex, multi-stage probability problems using Bayes' theorem. We'll tackle scenarios involving dice throws followed by coin tosses, selecting from a set of special coins (two-headed, biased, and fair), and a problem where a card is lost from a deck before two other cards are drawn. These examples showcase the power of Bayes' theorem in working backward from an observed outcome to find the probability of an initial state. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Using Bayes theorem for Dice, coins, and cards In this video, we solve a series of complex, multi-stage probability problems using Bayes' theorem. We'll tackle scenarios involving dice throws followed by coin tosses, selecting from a set of special coins (two-headed, biased, and fair), and a problem where a card is lost from a deck before two other cards are drawn. These examples showcase the power of Bayes' theorem in working backward from an observed outcome to find the probability of an initial state. https://cdn.kastatic.org/ka-youtube-converted/M1ileSyDayM.mp4/M1ileSyDayM.mp4 504 Solving probability using the laws of probability and Bayes' rule. https://www.khanacademy.org/math/ka-math-class-12/x6f66cbee9a2f805b:probability-ncert-new/x6f66cbee9a2f805b:applications-of-bayes-theorem/v/bayes-theorem-for-more-than-2-branches 2025-06-01T14:50:00.385158177Z Bayes theorem for more than 2 branches In this video, we extend our use of Bayes' theorem to scenarios involving more than two initial possibilities or ""branches."" We'll solve problems where a random choice is made from three or four different boxes, each containing a different mix of items. Given the outcome of a single draw, we will calculate the probability that it originated from each of the possible boxes. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Bayes theorem for more than 2 branches In this video, we extend our use of Bayes' theorem to scenarios involving more than two initial possibilities or ""branches."" We'll solve problems where a random choice is made from three or four different boxes, each containing a different mix of items. Given the outcome of a single draw, we will calculate the probability that it originated from each of the possible boxes. https://cdn.kastatic.org/ka-youtube-converted/G0PxZBEoOSg.mp4/G0PxZBEoOSg.mp4 381 Solving probability using the laws of probability and Bayes' rule. https://www.khanacademy.org/math/statistics-probability/probability-library/multiplication-rule-dependent/e/dependent_probability 2025-05-05T08:14:25.350149109Z Dependent probability Find dependent probabilities like P(A | B) or P(B | A) for a variety of contexts. Omar Rizwan exercise https://www.khanacademy.org/math/ka-math-class-12/x6f66cbee9a2f805b:probability-ncert-new/x6f66cbee9a2f805b:applications-of-bayes-theorem/e/baye-s-theorem-for-more-than-2-branches 2025-08-08T02:45:51.78671331Z Baye's theorem for more than 2 branches Baye's theorem for more than 2 branches Ashish Gupta exercise https://www.khanacademy.org/math/ka-math-class-12/x6f66cbee9a2f805b:probability-ncert-new/x6f66cbee9a2f805b:applications-of-bayes-theorem/e/applying-baye-s-theorem-in-other-scenarios 2025-08-08T02:45:51.78671331Z Applying Baye's theorem in other scenarios Applying Baye's theorem in other scenarios Ashish Gupta exercise