#P02 · Probability, Statistics & AI · Lv.2View in 3D Mind-Map

Conditional Probability & Chain Rule

Andrey Kolmogorov & Pierre-Simon Laplace · 1933 CE

P(A \mid B) = \frac{P(A \cap B)}{P(B)}, \quad P(A \cap B) = P(B)P(A \mid B)

P(x_1, \dots, x_T) = \prod_{t=1}^T P(x_t \mid x_1, \dots, x_{t-1})

Defines the probability of event A given that event B has occurred, shrinking the sample space to B and enabling autoregressive probability chains.

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Prob P(A)

Prob P(B)

Joint Prob P(A∩B)

P(A\mid B) = \frac{0.25}{0.50} = 50.0\%

조건부확률 P(A | B)

50.00%

역조건부 P(B | A)

62.50%

독립성 판정 P(A)P(B)

0.200 (종속)

Prerequisite Path (4 STEP)

Click steps in order to follow the 3D neon path from basics to target.

ax + b = 0 \implies x = -\frac{b}{a}

(a+b)^2 = a^2 + 2ab + b^2

{}_nP_r = \frac{n!}{(n-r)!}

P(A \mid B) = \frac{P(A \cap B)}{P(B)}

비 오는 날(B) 우산을 들고 있을 확률 P(A|B)은 전체 날 중 '비도 오고 우산도 든 날(A∩B)'의 비율을 '비 오는 날(B)'의 비율로 나눈 값입니다.

Core equation of autoregressive LLMs (like GPT), predicting the next token via P(w_t | w_1...w_{t-1}).

#LLM Next-Token#Autoregressive AI#Markov Chains#Probabilistic Graphical Models

const pAgivenB = (pAB, pB) => pB > 0 ? pAB / pB : 0;