Probability is a Fraction of a Finite Set
A simplified definition: a probability is a fraction of a finite set. For example, in the 2024 GSS survey, of the 3,986 respondents, 42 were bankers. If we choose a person from this population at random, the probability that they are a bank teller is 1.054%.
"""
~/blog/content/mathematics $ uv run --project probability_and_stochastic_systems python -m probability_and_stochastic_systems.sample_space_and_probability.probability_defn
"""
from __future__ import annotations
import pandas as pd
from ..data.gss_2024.gss import gss_2024
def probability(A: pd.Series[bool]):
"""Computes the probability of a proposition, A."""
return A.mean()
def print_probability(A: pd.Series[bool], label: str):
print(f"{A.sum()} / {A.count()} are {label}; prob = {probability(A):.4g}")
print_probability((gss_2024["indus10"] == 6870), "bankers") # 0.01054
print_probability((gss_2024["polviews"] <= 3), "liberals") # 0.2958
print_probability((gss_2024["partyid"] <= 1), "democrats") # 0.3016
References
- 1. Probability — Think Bayes. Allen Downey. allendowney.github.io . Accessed Sep 17, 2026.
- About the GSS. gss.norc.org . Accessed Sep 17, 2026.
The General Social Survey (GSS) touts itself as the only full-probability, personal-interview survey designed to monitor changes in both social characteristics and attitudes currently being conducted in the US.