computing probabilities by counting
(2 hours to learn)
Sometimes probability calculations involve large numbers of outcomes with equal probabilities. In this case, we can compute probabilities by counting the number of outcomes, using formulas for permutations and combinations.
This concept has the prerequisites:
- Be able to compute probabilities of events using the formulas for the numbers of permutations and combinations.
Core resources (read/watch one of the following)
→ Khan Academy: Probability and Statistics
→ Sets, Counting, and Probability
Online lectures on basic probability theory.
- Lecture "Probability by counting and inclusion-exclusion"
- Lecture "Principles of counting"
→ BerkeleyX: Introduction to Statistics: Probability
An online course on basic probability.
- Lecture 1.3, "Multiplication rule,"
- Lecture 1.4, "Problem-solving techniques"
→ A First Course in Probability
An introductory probability textbook.
Location: Section 2.5, "Sample spaces having equally likely outcomes," pages 37-48
→ An Introduction to Probability Theory and its Applications
A classic introductory probability textbook.
- Section 2.1, "Preliminaries," pages 26-28
- Section 2.2, "Ordered samples," pages 28-30
- Section 2.3, "Examples," pages 30-32
- Section 2.4, "Subpopulations and partitions," pages 32-36
→ Mathematical Statistics and Data Analysis
An undergraduate statistics textbook.
Location: Section 1.4, "Computing probabilities: counting methods," pages 6-15
→ Probability and Statistics
An introductory textbook on probability theory and statistics.
- Section 1.7, "Counting methods," pages 22-27
- Section 1.8, "Combinatorial methods," pages 28-33
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