Conditional Probability

Japanese: 条件付確率 - じょうけんつきかくりつ（英語表記）conditional probability

To describe chance phenomena mathematically, events and their probabilities are used. Given two events A and B , the probability that B will occur under the condition that A has occurred is called conditional probability and written as P ( B / A ). It limits the scope of the chance phenomenon under consideration to A , considers A as the whole, and represents the proportion that B occupies within it, and is calculated as follows. If A and B are independent, P ( B / A ) is equal to P ( B ). The same is true when considering several conditions simultaneously or sequentially, _and the conditional probability P ( _B / _A1∩ …… ∩Ak ₎ of B occurring under the condition that A1 , A2 , …, Ak _have occurred is (assuming the denominator is not 0) .

Source: Heibonsha World Encyclopedia, 2nd Edition Information

Japanese:

偶然現象を数学的に記述するには，事象とその確率とが用いられる。二つの事象A,Bがあって，Aが起こったという条件のもとでBが起こる確率を条件付確率と呼んでP(B/A)のように書く。それは考える偶然現象をAの範囲に制限し，Aを全体とみなして，そこでBの占める割合を表すもので，により計算される。AとBが独立なら，P(B/A)はP(B)に等しい。いくつかの条件を同時あるいは逐次に考える場合も同様で，A₁,A₂，……，A_kが起こったという条件のもとで，Bの起こる条件付確率P(B/A₁∩……∩A_k)は，である(分母は0でないとする)。

出典　株式会社平凡社世界大百科事典第２版について　情報

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