Conjunctive Probability

Dated Sep 17, 2026; last modified on Sat, 03 Oct 2026

Definition

Given two propositions, \(A\) and \(B\), the conjunction \(A \cap B\) (read \(A\) and \(B\)) is true if both \(A\) and \(B\) are true, and false otherwise. Conjunction is commutative, i.e., \(\mathbb{P}(A \cap B) = \mathbb{P}(B \cap A)\).

from __future__ import annotations

import pandas as pd

from .probability_defn import probability


def conjunctive_probability(A: pd.Series[bool], B: pd.Series[bool]) -> float:
    # Given two Boolean series, the `&` operator computes their conjunction.
    return probability(A & B)