ANALYSIS #4,5 FROM YASHCHENKO OPTIONS 19-36 HERE: https://www.youtube.com/live/fO_8xGAB... Stream on BOBR: https://bobr.video/watch?v=358b0b79-0... Materials for the web: https://1.shkolkovo.online/public-sto... 🥇Six-month course of preparation for the Unified State Exam/Basic State Exam ⬇️ Unified State Exam: https://3.shkolkovo.online/na-poryado... Basic State Exam: https://3.shkolkovo.online/na-poryado... 10th grade: https://3.shkolkovo.online/na-poryado... Shkolkovo promotions and discounts 👉🏻 https://3.shkolkovo.online/special?ut... 📲TG channel on mathematics with MO👉🏻 https://t.me/MO_EGE 📲VK group👉🏻 https://vk.com/shkolkovo_math Mailing list of useful materials VK👉🏻 https://vk.com/app5898182_-185634090#... Our YouTube channels: Preparation for the 2025 Unified State Exam in Shkolkovo ✔️ Mathematics with MO and Russian language with TA (Shkolkovo main channel): / @shkolkovo ✔️ Maxim Koval. Vlog of a math teacher: / @kovalmo ✔️ Physics with AB: / @shkolkovo_phys ✔️ Biology with EB: / @shkolkovo_bio ✔️ Chemistry Mutagen: / @mutagenege ✔️ Social Science and History Histructor: / @histructor ✔️ History with AB: / @shkolkovo_history ✔️ English language: / @shkolkovo_english ✔️ Computer Science BU: / @infbu ✔️ Babaev Alipasha Expert of the Unified State Exam in Mathematics: / @egemath_expert Preparation for the 2025 OGE in Shkolkovo ✔️ Mathematics with AF and Russian language with CN (Preparation for the OGE): / @shkolkovo-oge ✔️ Biology OGE with EB: / @shkolkovo_bio ✔️ Physics OGE with GK: / @shkolkovogk ✔️ Social Science OGE with EK: / @kant_soc ✔️ Computer Science OGE with MS: / @shkolkovo_inf_oge Olympiad areas in Shkolkovo ✔️ Economics. Shkolkovo Olympiads: / @econbyshkolkovo ✔️ Olympiad Mathematics with DA: / @shkolkovo_olymp ✔️ Olympiad Physics with AB / @shkolkovo_phys Timestamps: 00:00 Hello everyone! How are we going to bot today? Options 1-2 #4 - incompatible events #5 - the shooter shoots at targets, a chain of events 05:15 B-1, #4 08:26 B-1, #5 17:51 About Bernoulli's formula 18:57 B-2, #4 20:20 B-2, #5 Options 3-4 #4 - 2 friends in one group. We distribute one, then the second #5 - lottery tickets. The opposite event, we buy tickets until we get the appropriate probability 24:23 B-3, #4 26:27 B-3, #5 35:50 B-4, #4 37:07 B-4, #5 Options 5-6 #4 - the Olympics, probability by definition #5 is marriage. Introduction of the unknown and a chain of events 45:13 B-5, #4 46:32 B-5, #5 52:30 B-6, #4 53:42 B-6, #5 Options 7-8 #5 - a cube. We count the number of outcomes, the probability by definition is 57:03 B-7, #4 - a round table, 1 boy between two girls ⇒ we seat one girl, then the second 59:48 B-7, #5 01:02:52 B-8, #4 - a round table, 2 boys next to each other ⇒ we seat one boy, then the second 01:04:25 B-8, #5 Options 9-10 #4 - athletes from different countries, the probability of performing first/second. By definition 01:09:08 B-9, #4 01:11:16 B-9, #5 - a lottery, we take 4 tickets, we want exactly 1 winning one. Chain of events 01:21:03 B-10, #4 01:22:14 B-10, #5 - lottery, we take 3 tickets, we want at least 1 winning one. Chain of events Options 11-12 #4 - probability of coming in third/second. Probability by definition #5 - saucers and cups, we make 2 tea pairs. Many events, chain and score 01:30:40 B-11, #4 01:32:17 B-11, #5 01:54:40 B-12, #4 01:55:11 B-12, #5 Options 13-14 #4 - tourists fly in a helicopter. Probability by definition #5 - find the ratio of probabilities of events 02:04:35 B-13, #4 02:05:57 B-13, #5 - shooter 02:19:57 COMBINATORICS 02:27:53 Example for practicing combinatorics 02:32:02 B-14, #4 02:33:10 B-14, #5 - coin Options 15-16 #4 - bags with defects. Probability by definition #5 - felt-tip pens 02:44:23 B-15, #4 02:45:20 B-15, #5 02:48:39 B-16, #4 02:50:25 B-16, #5 Options 17-18 #4 - tickets by topic, probability by definition #5 - cubes (analogous to saucers) 02:53:08 B-17, #4 02:55:49 B-17, #5 03:05:25 Algorithm for solving the problem about saucers 03:06:04 B-18, #4 03:07:14 B-18, #5 - a setup! MO is joking 03:18:05 THAT'S IT! Half of the collection is done! Results, plans for the future and botat sochik!