Fundamentals of Probability and Independence

📋 Course Outline

1. Purpose of probability and conditional focus
2. Frequencies in contingency tables
3. Probabilistic vocabulary: experiments and events
4. Conditional probability definition and interpretation
5. Weighted probability trees and path rules
6. Total probability formula and tree inversion
7. Independence of events and product rule

📖 1. Purpose of probability and conditional focus

🔑 Key Concepts & Definitions

• Rationalizing chance : Probability is used to quantify the likelihood of outcomes produced by a random experiment.
• Random experiment : A random experiment is a procedure whose outcome cannot be predicted in advance.
• Conditional probabilities : Conditional probabilities are probabilities computed after restricting the situation using extra information.
• Contingency table : A contingency table cross-tabulates two characteristics of a population using counts in each cell.

📝 Essential Points

• Probability originated from gambling problems such as card and dice games.
• Modern probability is used in many fields like finance, insurance, medicine, and accident analysis.
• From earlier studies, students learn general methods such as reading tables and building probability trees.
• This chapter introduces a new type of probability: probabilities conditioned on additional information.
• Conditional probability calculations require restricting the reference universe to a subset defined by the condition.