Chapter 8. Probability and Risk

Summary

• The Logic of Probability: We distinguish between Objective Probability (how often things actually happen) and Subjective Probability (our degree of belief). We explore why human intuition fails in cases like the Gambler’s Fallacy and the Conjunction Fallacy.

• Statistical Generalizations: We examine how to move logically from a Sample to a Population. Strength in these arguments depends on three pillars: Size, Representativeness, and Randomness.

• The Measures of Average: We deconstruct the “Average” to show how the Mean, Median, and Mode can be used to tell very different stories from the same data set.

• Risk and Decision Theory: We apply the Expected Value (EV) formula to rational choices and contrast it with Prospect Theory, which explains why humans are naturally loss-averse and easily misled by “vivid” risks.

Key Terms

• Availability Heuristic: A mental shortcut where we judge the probability of an event based on how easily we can recall an example (leading to an overestimation of “vivid” risks like plane crashes).

• Base Rate Neglect: The logical error of ignoring the background frequency of an event (the “base rate”) in favor of specific, often misleading, new information.

• Bayes’ Theorem: A mathematical formula used to update the probability of a hypothesis as more evidence or information becomes available.

• Confidence Level: The probability that the results of a sample accurately represent the population within the margin of error (standardly set at 95%).

• Conjunction Fallacy: The mistaken belief that two specific conditions occurring together are more probable than a single, general condition.

• Expected Value (EV): The “rational” value of an uncertain outcome, calculated by multiplying the probability of the event by its value or cost.

• Gambler’s Fallacy: The mistaken belief that independent past events (like coin flips) influence the probability of future independent events.

• Margin of Error: The range of possible values above and below a sample statistic that likely contains the true population value.

• Mean: The arithmetic average, calculated by dividing the total sum by the number of cases; highly sensitive to outliers.

• Median: The middle point in a distribution; the most “robust” measure of central tendency for skewed data like income.

• Mode: The most frequently occurring value in a data set.

• Prospect Theory: A psychological theory describing how people choose between probabilistic alternatives that involve risk, highlighting that we value losses and gains differently.

• Standard Deviation: A measure of the amount of variation or dispersion in a set of values; how “spread out” the data is from the mean.