https://www.khanacademy.org/math/ka-math-class-12/x6f66cbee9a2f805b:probability-ncert-new/x6f66cbee9a2f805b:independent-events/v/independent-events-dice-thrown-and-balls-picked 2025-06-01T14:50:00.385158177Z Independent events (dice thrown and balls picked) In this video, we apply the concept of independent events to solve practical probability problems. We'll first tackle a problem involving tossing a die three times and finding the probability of getting an odd number at least once, by considering the complementary event. Then, we'll analyze a scenario where two balls are drawn at random with replacement from a box containing black and red balls, and calculate probabilities for different outcomes like both balls being red, or one being black and the other red. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Independent events (dice thrown and balls picked) In this video, we apply the concept of independent events to solve practical probability problems. We'll first tackle a problem involving tossing a die three times and finding the probability of getting an odd number at least once, by considering the complementary event. Then, we'll analyze a scenario where two balls are drawn at random with replacement from a box containing black and red balls, and calculate probabilities for different outcomes like both balls being red, or one being black and the other red. https://cdn.kastatic.org/ka-youtube-converted/Y5jIO9f_8zU.mp4/Y5jIO9f_8zU.mp4 276 Exploring independent events and probability involving it https://www.khanacademy.org/math/ka-math-class-12/x6f66cbee9a2f805b:probability-ncert-new/x6f66cbee9a2f805b:independent-events/v/independent-events-other-scenarios 2025-06-01T14:50:00.385158177Z Independent events (other scenarios) This video covers more application scenarios involving independent and conditional probabilities. We'll analyze a problem where two individuals, A and B, try to solve a problem independently, and calculate the probability that the problem is solved and the probability that exactly one of them solves it. Another example involves students' newspaper reading habits, where we find probabilities such as a student reading neither Hindi nor English newspapers, or reading English given they read Hindi. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Independent events (other scenarios) This video covers more application scenarios involving independent and conditional probabilities. We'll analyze a problem where two individuals, A and B, try to solve a problem independently, and calculate the probability that the problem is solved and the probability that exactly one of them solves it. Another example involves students' newspaper reading habits, where we find probabilities such as a student reading neither Hindi nor English newspapers, or reading English given they read Hindi. https://cdn.kastatic.org/ka-youtube-converted/SRUbP25ser8.mp4/SRUbP25ser8.mp4 373 Exploring independent events and probability involving it https://www.khanacademy.org/math/ap-statistics/probability-ap/stats-conditional-probability/v/testing-independence-from-experimental-data 2022-10-07T00:58:19.561984208Z Conditional probability and independence Use conditional probability to see if events are independent or not. video https://cdn.kastatic.org/ka_thumbnails_cache/3750f6c6-8a29-4f71-a181-6c754f0e152f_1280_720_base.png Conditional probability and independence Use conditional probability to see if events are independent or not. https://cdn.kastatic.org/ka-youtube-converted/pIfpHdGVwLU.mp4/pIfpHdGVwLU.mp4 247 Exploring independent events and probability involving it https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:prob-comb/x9e81a4f98389efdf:compound-probability-of-ind-events-using-mult-rule/v/independent-events-2 2021-07-01T17:39:51Z Independent events example: test taking Have you ever taken a test and discovered you have no choice but to guess on a couple of problems? In this example problem, we are considering the probability of two independent events occurring. Sal Khan video https://cdn.kastatic.org/googleusercontent/yenbmoo4Av9R4p2biWUvxRjFq_WvZCkw0h37aT3Bs80AKh76ZA8rqaNTK3319ySkiFT-1XROwmyjqrWcaTpKWOnE Independent events example: test taking Have you ever taken a test and discovered you have no choice but to guess on a couple of problems? In this example problem, we are considering the probability of two independent events occurring. https://cdn.kastatic.org/ka-youtube-converted/VWAfEbgf1Po.mp4/VWAfEbgf1Po.mp4 284 Exploring independent events and probability involving it https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:prob-comb/x9e81a4f98389efdf:compound-probability-of-ind-events-using-mult-rule/v/compound-probability-of-independent-events 2023-04-15T06:53:33.172253602Z Compound probability of independent events Learn how to calculate probabilities of coin flips using two methods: listing all possible outcomes or multiplying independent events. Understand what independent events are and how to avoid the gambler's fallacy. Review fractions and how the sum of all probabilities equals one. Sal Khan video https://cdn.kastatic.org/googleusercontent/U9uGqrrUK5Me3KOS3D8ICYUOL4Ko9Z7M0Ai7bLg_CNZVz3Zg1mVQ3qJliUifwuLpv6C6oi_wGUnbfE1P7Vdwc6Rg Compound probability of independent events Learn how to calculate probabilities of coin flips using two methods: listing all possible outcomes or multiplying independent events. Understand what independent events are and how to avoid the gambler's fallacy. Review fractions and how the sum of all probabilities equals one. https://cdn.kastatic.org/ka-youtube-converted/xSc4oLA9e8o.mp4/xSc4oLA9e8o.mp4 360 Exploring independent events and probability involving it https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:prob-comb/x9e81a4f98389efdf:compound-probability-of-ind-events-using-mult-rule/v/general-multiplication-example-independent 2022-10-07T00:22:18.752150461Z General multiplication rule example: independent events We can use the general multiplication rule to find the probability that two events both occur when the events are independent. Sal Khan video https://cdn.kastatic.org/ka_thumbnails_cache/af2b44b8-104e-4b95-b809-7cd74308a22c_1280_720_base.png General multiplication rule example: independent events We can use the general multiplication rule to find the probability that two events both occur when the events are independent. https://cdn.kastatic.org/ka-youtube-converted/OqbkCYy37hI.mp4/OqbkCYy37hI.mp4 149 Exploring independent events and probability involving it https://www.khanacademy.org/math/statistics-probability/probability-library/conditional-probability-independence/v/independent-dependent-probability 2021-04-12T12:34:14Z Analyzing event probability for independence Sal uses an example about shirts, scarves, hats, and pants to explain how to use probabilities to figure out if two events are independent. Sal Khan video https://cdn.kastatic.org/googleusercontent/Da5LDWZmjVlwspAjtEGGl5wXgYO5oIFMy94CXvwSS08PGi6PpA722WDCK62Y638IWkmNaoNXkBayDN0UnNdU-iw0uw Analyzing event probability for independence Sal uses an example about shirts, scarves, hats, and pants to explain how to use probabilities to figure out if two events are independent. https://cdn.kastatic.org/ka-youtube-converted/R-NeYKSEqns.mp4/R-NeYKSEqns.mp4 408 Exploring independent events and probability involving it https://www.khanacademy.org/math/ap-statistics/probability-ap/stats-conditional-probability/a/check-independence-conditional-probability 2021-07-01T17:39:48Z Conditional probability and independence article https://www.khanacademy.org/math/statistics-probability/probability-library/conditional-probability-independence/e/identifying-dependent-and-independent-events 2026-04-07T22:59:30.107127435Z Dependent and independent events Determine if two events are dependent or independent. Ben Lucki exercise https://www.khanacademy.org/math/statistics-probability/probability-library/multiplication-rule-independent/e/independent_probability 2025-04-08T07:26:09.960930891Z Independent probability Find probabilities of independent events like flipping a heads and rolling an even number! Ben Eater exercise