United University

Algebra Grade 11. Elements of combinatorics and probability theory. Collection 1

Course Difficulty Icon Intermediate
Course Type Icon Course
Course Duration Icon 13 годин

Explore the fascinating world of combinatorics and probability! This course introduces students to combinations, permutations, arrangements, random events, classical probability, combinatorial schemes, and basic statistical measures such as range, mode, median, and mean.

The course includes interactive tests with automatic grading, homework, and review exercises, allowing students to reinforce their knowledge and develop problem-solving and analytical skills in practical contexts.

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Explore the fascinating world of combinatorics and probability! Our "Algebra Grade 11. Elements of combinatorics and probability theory. Collection 1" course provides students with fundamental knowledge in combinatorics, probability, and statistics. Learners will study combinations, permutations, arrangements, random events, classical probability definitions, combinatorial schemes, and statistical measures such as range, mode, median, and mean.

Why choose our course:

  • Interactive tests and exercises: Reinforce your understanding with homework assignments, review tasks, and self-check exercises with automatic grading.
  • Expertly structured content: Aligned with the State Standard of Basic Secondary Education and model educational programs for Grade 11.
  • Practical and analytical focus: Develop the ability to calculate probabilities, analyze random events, and apply statistical measures to real-world situations.

Course Modules

Module 3: Elements of combinatorics and probability theory

  • §16. Sets and their elements
  • §16. Sets and their elements (Part 1)
  • §16. Sets and their elements (Part 2)
  • Knowledge check for §16
  • §17. Elements of combinatorics. Arrangements, permutations, combinations
  • §17. Elements of combinatorics. Arrangements, permutations, combinations (Part 1)
  • §17. Elements of combinatorics. Arrangements, permutations, combinations (Part 2)
  • Knowledge check for §17
  • §18. Random experiment and random event. Probability of an event
  • §18. Random experiment and random event. Probability of an event (Part 1)
  • §18. Random experiment and random event. Probability of an event (Part 2)
  • §18. Random experiment and random event. Probability of an event (Part 3)
  • Knowledge check for §18
  • Homework assignment №6
  • Knowledge check tasks for §§16–18
  • §19. Operations on events. Axioms of probability and main consequences
  • §19. Operations on events. Axioms of probability and main consequences (Part 1)
  • §19. Operations on events. Axioms of probability and main consequences (Part 2)
  • §19. Operations on events. Axioms of probability and main consequences (Part 3)
  • Knowledge check for §19
  • §20. Independent events. Conditional probability
  • §20. Independent events. Conditional probability (Part 1)
  • §20. Independent events. Conditional probability (Part 2)
  • Knowledge check for §20
  • §21. Random variable and its expected value
  • §21. Random variable and its expected value (Part 1)
  • Knowledge check for §21
  • Homework assignment №7
  • Knowledge check tasks for §§19–21
  • Revision exercises for Module 3 (§16–§17)
  • Revision exercises for Module 3 (§18–§19)
  • Revision exercises for Module 3 (§20–§21)
  • Ukrainian Women in the World

Expected Learning Outcomes

  • Understand permutations, arrangements, combinations, classical probability, population and sample concepts, mean, mode, and median.
  • Calculate relative frequency, number of permutations, arrangements, combinations, and probability of events using definitions and combinatorial schemes.
  • Interpret statistical measures and sample characteristics.
  • Find numerical characteristics of given data samples.
  • Apply probabilistic characteristics of real-world phenomena for decision-making.

By the end of this course, students will have a strong foundation in combinatorics, probability, and statistics, be able to compute probabilities and combinatorial counts, analyze random events, and apply statistical measures in practical contexts, preparing them for advanced studies and problem-solving in real life.

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