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Sample Spaces and the Counting Principle

Algebra Foundation

Algebra 2

Explore advanced functions, complex numbers, polynomials, rational and radical expressions, exponentials, logarithms, conics, sequences, introductory trigonometry, probability, and statistics.

Learn with original explanations and worked examples. OpenStax Intermediate Algebra 2e was consulted for topic coverage.

Study every current unit through original concept lessons, formula derivations, experiments, quizzes, and practice sets.

Algebra 2 · Unit 11 · Topic 11.1

Sample Spaces and the Counting Principle

A sample space lists the possible outcomes.

Definition and explanation

A sample space lists the possible outcomes. For a sequence of choices where each stage has the stated number of options for every earlier choice, multiply the option counts to find the number of combined outcomes.

Worked example

An identification code has one of 4 letters followed by two digits from 0 through 9, with repetition allowed. There are 4 × 10 × 10 = 400 codes. Allowing the same digit twice is essential to this count.

Common mistake

Multiplication counts combinations of choices; adding the option counts would count a different situation.

Key takeaway

A sample space lists the possible outcomes.

Explain each step of the worked example, then check the units, signs, and conditions that apply.

Further reading

Topic coverage was checked against the openly available OpenStax Intermediate Algebra 2e, Algebra and Trigonometry 2e, and Introductory Statistics 2e textbooks. The explanations and examples on this site are independently written; textbook prose, exercises, and artwork are not reproduced.