(1) Video Library > 7. Reasoning About Chance and Uncertainty: Philosophy, Rules and Fallacies
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Introduction
Introduction
Part 1: What is Probability?: A Gentle Introduction to the Philosophy of Probability
Introduction
What is Probability?
Probability: Why Learn This Stuff?
What is Inductive Logic?
Probability as a Mathematical Object vs What That Object Represents
Interpretations of Probability
Classical Probability
Logical Probability
Frequency Interpretations
Subjective (Bayesian) Probability
Propensity Interpretations
Part 2: The Logic of Probability: Introduction to the Basic Rules
Introduction
Preliminary Concepts
What Has a Probability? Propositions versus Events
Probabilities Range Between 0 and 1
Mutually Exclusive Events
Independent Events
The Basic Rules
The Negation Rule: P(not-A)
Disjunction Rules: P(A or B)
Restricted Disjunction Rule: P(A or B) = P(A) + P(B)
General Disjunction Rule: P(A or B) = P(A) + P(B) - P(A and B)
Conjunction Rules: P(A and B)
Restricted Conjunction Rule: P(A and B) = P(A) x P(B)
General Conjunction Rule: P(A and B) = P(A) x P(B|A)
Conditional Rules: P(A given B)
Conditional Probability Rule
Total Probability Rule
Bayes’ Rule
Part 3: Probability Fallacies: Understanding the Errors We Make When Reasoning About Chance and Uncertainty
Introduction
Coincidences: When the Impossible Becomes Inevitable
Introduction
The Basic Fallacy
Borel's Law: Understanding Impossible Events
How to Create the Illusion of Miraculous Predictive Power
The Birthday Problem, Lottery Coincidences and the Power of Very Large Numbers
The Gambler's Fallacy: Bias, Randomness and the Illusion of Control
Introduction
The Basic Fallacy
Fairness, Bias and Independence
How Can You Tell Whether a Chance Setup is Unfair?
The Physics of Coin Tosses
Casino Games: Why the House Always Wins
Cognitive Factors and the Psychology of Gambling
Small Sample Fallacies: Looking for Causes of Extreme Cases
The Small Sample Fallacy: Looking for Causes of Statistical Artifacts
Products
Course
Section
Disjunction Rules: P(A or B)
Disjunction Rules: P(A or B)
(1) Video Library > 7. Reasoning About Chance and Uncertainty: Philosophy, Rules and Fallacies
Buy now
Learn more
Introduction
Introduction
Part 1: What is Probability?: A Gentle Introduction to the Philosophy of Probability
Introduction
What is Probability?
Probability: Why Learn This Stuff?
What is Inductive Logic?
Probability as a Mathematical Object vs What That Object Represents
Interpretations of Probability
Classical Probability
Logical Probability
Frequency Interpretations
Subjective (Bayesian) Probability
Propensity Interpretations
Part 2: The Logic of Probability: Introduction to the Basic Rules
Introduction
Preliminary Concepts
What Has a Probability? Propositions versus Events
Probabilities Range Between 0 and 1
Mutually Exclusive Events
Independent Events
The Basic Rules
The Negation Rule: P(not-A)
Disjunction Rules: P(A or B)
Restricted Disjunction Rule: P(A or B) = P(A) + P(B)
General Disjunction Rule: P(A or B) = P(A) + P(B) - P(A and B)
Conjunction Rules: P(A and B)
Restricted Conjunction Rule: P(A and B) = P(A) x P(B)
General Conjunction Rule: P(A and B) = P(A) x P(B|A)
Conditional Rules: P(A given B)
Conditional Probability Rule
Total Probability Rule
Bayes’ Rule
Part 3: Probability Fallacies: Understanding the Errors We Make When Reasoning About Chance and Uncertainty
Introduction
Coincidences: When the Impossible Becomes Inevitable
Introduction
The Basic Fallacy
Borel's Law: Understanding Impossible Events
How to Create the Illusion of Miraculous Predictive Power
The Birthday Problem, Lottery Coincidences and the Power of Very Large Numbers
The Gambler's Fallacy: Bias, Randomness and the Illusion of Control
Introduction
The Basic Fallacy
Fairness, Bias and Independence
How Can You Tell Whether a Chance Setup is Unfair?
The Physics of Coin Tosses
Casino Games: Why the House Always Wins
Cognitive Factors and the Psychology of Gambling
Small Sample Fallacies: Looking for Causes of Extreme Cases
The Small Sample Fallacy: Looking for Causes of Statistical Artifacts
2 Lessons
Restricted Disjunction Rule: P(A or B) = P(A) + P(B)
General Disjunction Rule: P(A or B) = P(A) + P(B) - P(A and B)