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Probability Theory Study Guide

A comprehensive guide to understanding probability theory, covering single events, compound events (AND/OR logic), conditional probability, and dependent events. Includes formulas and worked examples for dice rolls, coin flips, and marble draws.

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Counting and Probability

Permutations

Calculating the number of ways to arrange items where order matters. This includes permutations of a whole set (n!), permutations of a subset (nPr), and permutations with repetitions.

  • Order matters
  • Factorial notation
  • nPr formula
  • Permutations with repetition
  • Arrangements
  • Sequences

Probability Theory

Core principles of calculating the probability of single and compound events.

  • Sample space
  • Favorable outcomes
  • Probability formula
  • Independent events
  • Dependent events
  • Mutually exclusive events
  • Conditional probability
  • Multiplication rule
  • Addition rule

Probability Applications

Applying counting and probability rules to solve real-world mathematical problems.

  • Coin flips
  • Dice rolls
  • Sampling without replacement
  • Weather forecasting
  • Financial modeling

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