https://www.khanacademy.org/math/ka-math-class-12/x6f66cbee9a2f805b:probability-ncert-new/x6f66cbee9a2f805b:properties-of-conditional-probability/v/properties-of-conditional-probability 2025-06-01T14:50:00.385158177Z Properties of conditional probability In this video, we explore the fundamental properties of conditional probability. We'll cover three key properties: First, the probability of the sample space or the event itself, given an event F, is always 1. Second, the addition rule for conditional probability for the union of two events. And third, the relationship between the conditional probability of an event and its complement. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Properties of conditional probability In this video, we explore the fundamental properties of conditional probability. We'll cover three key properties: First, the probability of the sample space or the event itself, given an event F, is always 1. Second, the addition rule for conditional probability for the union of two events. And third, the relationship between the conditional probability of an event and its complement. https://cdn.kastatic.org/ka-youtube-converted/BZ5e_lv2o1k.mp4/BZ5e_lv2o1k.mp4 444 Properties of Conditional probability https://www.khanacademy.org/math/ka-math-class-12/x6f66cbee9a2f805b:probability-ncert-new/x6f66cbee9a2f805b:properties-of-conditional-probability/v/applying-properties-of-conditional-probability 2025-06-01T14:50:00.385158177Z Applying properties of conditional probability In this video, we apply the fundamental properties of conditional probability to solve various problems. We'll use the formula P(A|B) = P(A intersect B) / P(B) to calculate conditional probabilities when the probabilities of individual events and their intersection or union are known. We work through several examples demonstrating how to find P(E|F), P(F|E), P(A intersect B), P(A|B), and P(A U B) under different given conditions. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Applying properties of conditional probability In this video, we apply the fundamental properties of conditional probability to solve various problems. We'll use the formula P(A|B) = P(A intersect B) / P(B) to calculate conditional probabilities when the probabilities of individual events and their intersection or union are known. We work through several examples demonstrating how to find P(E|F), P(F|E), P(A intersect B), P(A|B), and P(A U B) under different given conditions. https://cdn.kastatic.org/ka-youtube-converted/YLlAd-auuHw.mp4/YLlAd-auuHw.mp4 298 Properties of Conditional probability https://www.khanacademy.org/math/ka-math-class-12/x6f66cbee9a2f805b:probability-ncert-new/x6f66cbee9a2f805b:properties-of-conditional-probability/e/applying-properties-of-conditional-probability-3 2025-08-08T02:45:51.78671331Z Applying properties of conditional probability Applying properties of conditional probability Ashish Gupta 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-1/v/finding-probability-of-an-event-given-another 2025-06-01T14:50:00.385158177Z Finding probability of an event given another This video focuses on calculating conditional probabilities P(E|F) by first defining the sample space and the specific events E and F. We'll work through examples involving tossing a coin three times with various conditions for E and F, tossing two coins once, and a scenario where a mother, father, and son line up for a family picture. For each problem, we identify the outcomes in E, F, and their intersection to find P(E|F). Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Finding probability of an event given another This video focuses on calculating conditional probabilities P(E|F) by first defining the sample space and the specific events E and F. We'll work through examples involving tossing a coin three times with various conditions for E and F, tossing two coins once, and a scenario where a mother, father, and son line up for a family picture. For each problem, we identify the outcomes in E, F, and their intersection to find P(E|F). https://cdn.kastatic.org/ka-youtube-converted/GlrEmizXX8g.mp4/GlrEmizXX8g.mp4 546 Properties of Conditional probability https://www.khanacademy.org/math/ka-math-class-12/x6f66cbee9a2f805b:probability-ncert-new/x6f66cbee9a2f805b:properties-of-conditional-probability/e/finding-probability-of-an-event-given-another 2025-08-08T02:45:51.78671331Z Finding probability of an event given another Finding probability of an event given another Ashish Gupta exercise https://www.khanacademy.org/math/ka-math-class-12/x6f66cbee9a2f805b:probability-ncert-new/x6f66cbee9a2f805b:properties-of-conditional-probability/v/elementary-events-equally-likely 2025-06-01T14:50:00.385158177Z Elementary events equally likely In this video, we solve conditional probability problems where all elementary outcomes in the sample space are equally likely. We'll look at scenarios like a die being thrown multiple times, with specific conditions defining events A and B, and then find P(A|B). Examples include finding the probability of a '4 on the third throw' given '6 on the first and 5 on the second', and the probability that 'number 4 appeared at least once' given the 'sum of numbers is 6' when a die is thrown twice. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Elementary events equally likely In this video, we solve conditional probability problems where all elementary outcomes in the sample space are equally likely. We'll look at scenarios like a die being thrown multiple times, with specific conditions defining events A and B, and then find P(A|B). Examples include finding the probability of a '4 on the third throw' given '6 on the first and 5 on the second', and the probability that 'number 4 appeared at least once' given the 'sum of numbers is 6' when a die is thrown twice. https://cdn.kastatic.org/ka-youtube-converted/ZkJ7tKYXJbs.mp4/ZkJ7tKYXJbs.mp4 327 Properties of Conditional probability https://www.khanacademy.org/math/ka-math-class-12/x6f66cbee9a2f805b:probability-ncert-new/x6f66cbee9a2f805b:properties-of-conditional-probability/e/elementary-events-equally-likely 2025-08-08T02:45:51.78671331Z Elementary events equally likely Elementary events equally likely Ashish Gupta exercise https://www.khanacademy.org/math/ka-math-class-12/x6f66cbee9a2f805b:probability-ncert-new/x6f66cbee9a2f805b:properties-of-conditional-probability/v/conditional-probability-other-scenarios 2025-06-01T14:50:00.385158177Z Conditional probability - other scenarios This video covers various word problems that can be solved using conditional probability. We'll tackle scenarios such as drawing a numbered card and finding the probability of it being even given it's more than 3. Another problem involves finding the probability that a randomly chosen student studies in Class XII given the student is a girl. We also calculate the probability of a question being easy given it's a multiple-choice question from a mixed question bank. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Conditional probability - other scenarios This video covers various word problems that can be solved using conditional probability. We'll tackle scenarios such as drawing a numbered card and finding the probability of it being even given it's more than 3. Another problem involves finding the probability that a randomly chosen student studies in Class XII given the student is a girl. We also calculate the probability of a question being easy given it's a multiple-choice question from a mixed question bank. https://cdn.kastatic.org/ka-youtube-converted/mQ5hp8zP6eA.mp4/mQ5hp8zP6eA.mp4 323 Properties of Conditional probability