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 Applications of Bayes' theorem 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 Applications of Bayes' theorem 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/v/probability-of-the-transferred-ball 2025-06-01T14:50:00.385158177Z Probability of the transferred ball This video focuses on a classic two-stage probability problem involving the transfer of an item between two groups. We'll analyze a scenario where one ball is transferred from Box I to Box II, changing the composition of Box II, before a second ball is drawn from it. Using a tree diagram and Bayes' theorem, we will calculate the probability of the transferred ball's color, given the color of the ball drawn from the second box. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Probability of the transferred ball This video focuses on a classic two-stage probability problem involving the transfer of an item between two groups. We'll analyze a scenario where one ball is transferred from Box I to Box II, changing the composition of Box II, before a second ball is drawn from it. Using a tree diagram and Bayes' theorem, we will calculate the probability of the transferred ball's color, given the color of the ball drawn from the second box. https://cdn.kastatic.org/ka-youtube-converted/d_s0ypk6hCM.mp4/d_s0ypk6hCM.mp4 328 Applications of Bayes' theorem https://www.khanacademy.org/math/ka-math-class-12/x6f66cbee9a2f805b:probability-ncert-new/x6f66cbee9a2f805b:applications-of-bayes-theorem/v/probability-of-positive-determinant 2025-06-01T14:50:00.385158177Z Probability of positive determinant In this video, we tackle a unique problem that combines probability theory with linear algebra. We'll consider a 2x2 determinant where each element is chosen randomly to be either zero or one. We will calculate the total number of possible determinants, and then find the probability that the value of the determinant is positive. We'll also explore related conditional probabilities. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Probability of positive determinant In this video, we tackle a unique problem that combines probability theory with linear algebra. We'll consider a 2x2 determinant where each element is chosen randomly to be either zero or one. We will calculate the total number of possible determinants, and then find the probability that the value of the determinant is positive. We'll also explore related conditional probabilities. https://cdn.kastatic.org/ka-youtube-converted/MK0FVX-bJcA.mp4/MK0FVX-bJcA.mp4 376 Applications of Bayes' theorem https://www.khanacademy.org/math/ka-math-class-12/x6f66cbee9a2f805b:probability-ncert-new/x6f66cbee9a2f805b:applications-of-bayes-theorem/v/finding-probability-in-other-scenarios 2025-06-01T14:50:00.385158177Z Finding probability in other scenarios This video tackles a couple of interesting and classic probability problems. First, we apply Bayes' theorem to a scenario involving different physical traits in men and women. Given that a randomly selected person has grey hair, we calculate the probability that the person is male. Next, we solve the well-known puzzle of determining the probability that a randomly selected leap year will contain 53 Tuesdays by analyzing the possible combinations for the two extra days. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Finding probability in other scenarios This video tackles a couple of interesting and classic probability problems. First, we apply Bayes' theorem to a scenario involving different physical traits in men and women. Given that a randomly selected person has grey hair, we calculate the probability that the person is male. Next, we solve the well-known puzzle of determining the probability that a randomly selected leap year will contain 53 Tuesdays by analyzing the possible combinations for the two extra days. https://cdn.kastatic.org/ka-youtube-converted/J9k3U4nJi38.mp4/J9k3U4nJi38.mp4 310 Applications of Bayes' theorem 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 https://www.khanacademy.org/math/ka-math-class-12/x6f66cbee9a2f805b:probability-ncert-new/x6f66cbee9a2f805b:applications-of-bayes-theorem/v/probabilities-in-an-infinite-game 2025-06-01T14:50:00.385158177Z Probabilities in an infinite game In this video, we analyze the probabilities of winning a game that could potentially continue infinitely. We'll focus on a classic example where two players, A and B, take turns throwing a die, with the first to roll a '6' declared the winner. We will calculate their respective probabilities of winning using two different powerful methods: setting up a recursive probability equation, and summing an infinite geometric series. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Probabilities in an infinite game In this video, we analyze the probabilities of winning a game that could potentially continue infinitely. We'll focus on a classic example where two players, A and B, take turns throwing a die, with the first to roll a '6' declared the winner. We will calculate their respective probabilities of winning using two different powerful methods: setting up a recursive probability equation, and summing an infinite geometric series. https://cdn.kastatic.org/ka-youtube-converted/A7zWvEC-Ib0.mp4/A7zWvEC-Ib0.mp4 380 Applications of Bayes' theorem https://www.khanacademy.org/math/ka-math-class-12/x6f66cbee9a2f805b:probability-ncert-new/x6f66cbee9a2f805b:applications-of-bayes-theorem/e/probabilities-in-an-infinite-game 2025-08-08T02:45:51.78671331Z Probabilities in an infinite game Probabilities in an infinite game Ashish Gupta exercise https://www.khanacademy.org/math/ka-math-class-12/x6f66cbee9a2f805b:probability-ncert-new/x6f66cbee9a2f805b:applications-of-bayes-theorem/v/conceptual-problems-in-probability 2025-06-01T14:50:00.385158177Z Conceptual problems in Probability This video tests your fundamental understanding of probability with a series of conceptual multiple-choice questions. We'll explore the implications of various conditions, such as: what happens to conditional probability when the given event has a probability of zero? What can be concluded if P(A|B) equals P(B|A)? What is the formal condition for the independence of two events? And if A is a subset of B, what is the relationship between P(A|B) and P(A)? Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Conceptual problems in Probability This video tests your fundamental understanding of probability with a series of conceptual multiple-choice questions. We'll explore the implications of various conditions, such as: what happens to conditional probability when the given event has a probability of zero? What can be concluded if P(A|B) equals P(B|A)? What is the formal condition for the independence of two events? And if A is a subset of B, what is the relationship between P(A|B) and P(A)? https://cdn.kastatic.org/ka-youtube-converted/UcJTMG4zzm0.mp4/UcJTMG4zzm0.mp4 428 Applications of Bayes' theorem https://www.khanacademy.org/math/ka-math-class-12/x6f66cbee9a2f805b:probability-ncert-new/x6f66cbee9a2f805b:applications-of-bayes-theorem/e/conceptual-problems-in-probability 2025-08-08T02:45:51.78671331Z Conceptual problems in Probability Conceptual problems in Probability Ashish Gupta exercise