Systematically count finite outcomes using organized lists, tables, and tree diagrams, applying the fundamental counting principle, addition and multiplication principles, permutations with or without repetition, and combinations while distinguishing ordered arrangements from unordered selections. Apply the binomial theorem for nonnegative integer powers, expanding , identifying terms and coefficients, and interpreting binomial coefficients as combination counts. Calculate probabilities in equally likely finite sample spaces using counting techniques, conditional probabilities, and complementary events, and determine whether events are independent or mutually exclusive using multiplication and conditional-probability rules.
On this page:
- Master skills like “Calculate combinations”, “Apply the binomial theorem”, and “Use organized counting strategies” with unlimited, free practice problems
- Download (or modify) free worksheets on Counting and Probability you can use at home or in class with practice problems across all skills in this group including “Calculate conditional probabilities”, “Apply the fundamental counting principle”, “Determine whether events are independent”.
- Start working on adaptive units like “Probability and Statistics - Binomial Notation Practice” or “Probability and Statistics - Permutation or Combination Concepts - Intro” that include these skills and will introduce and scaffold the skills carefully for maximum learning.
Counting and Probability: Individual Skills
Master 10 individual skills with free practice problems. Mouseover to see the skill's practice problems. Create a free account to track your progress.
Your results
- Apply the binomial theorem
- Apply the fundamental counting principle
- Calculate combinations
- Calculate conditional probabilities
- Calculate permutations with repeated elements
- Calculate permutations without repetition
- Calculate probabilities using counting techniques
- Determine whether events are independent
- Distinguish permutations from combinations
- Use organized counting strategies
Practice 'Apply the binomial theorem'
Select any skill in this group by hovering over the list above. Unlimited free practice problems, automatically graded.
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Download/Modify Free Grade 12 'Counting and Probability' Worksheet
Print this free 'Counting and Probability' worksheet to practice these skills away from the computer. Click 'Modify' to easily customize this worksheet to your exact needs.
This Worksheet Includes:
- Apply the binomial theorem
- Apply the fundamental counting principle
- Calculate combinations
- Calculate conditional probabilities
- Calculate permutations with repeated elements
- Calculate permutations without repetition
- Calculate probabilities using counting techniques
- Determine whether events are independent
Units Teaching These Skills
These adaptive units introduce, teach, or reinforce skills in this group (Counting and Probability) through scaffolded problems that grow in difficulty as concepts are understood.