Math & Statistics · 概率基础（Probability Basics） · Updated 2026-10-25
What Is Probability Basics?
Definition
Classical probability P(A) = favorable ÷ total (assuming equal likelihood). Core rules: addition for mutually exclusive events P(A∪B)=P(A)+P(B), generally P(A)+P(B)−P(A∩B); multiplication for independent events P(A∩B)=P(A)×P(B); complement P(at least one) = 1−P(none). "At least one head in 5 flips" = 1−(1/2)^5 ≈ 96.9% — the complement beats enumeration. Conditional probability P(A|B)=P(A∩B)/P(B) grounds Bayesian reasoning.
Formula
P(at least one) = 1 − (1−p)^n; P(A|B) = P(A∩B)/P(B)
Worked Example
Two 60% shooters firing at once: at least one hits with 1−0.4×0.4 = 84% — not 120% (probabilities cap at 100%).
Common Misconception
"Five tails in a row means heads is due" — the gambler's fallacy: independent events carry no memory. And small-sample frequency equals probability — 7 heads in 10 flips (70%) contradicts nothing; short samples swing wildly.
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