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conditional probability concept

DefinitionThe probability of A among the repetitions in which B occurred, the probability of both divided by the probability of B. Precision, recall, and calibration are each one. Primer S, equation S.2. Also conditional probabilit.
ExampleGiven that the first die shows three, the sum is seven only when the second shows four, probability one sixth.
BookData Mining as Observation, draft 0.2, commit f3914f0; entry id conditional-probability, kind concept.
Statusno ledger row names this entry. Corrections: none recorded.
Defining equation

Book equation S.2.

Assumptions and scopenone
Prior artnone recorded
Evidencenone
Reviewedsemantic review 2026-09-09; generated 2026-09-10 from records at the commits on the provenance page.

Equation

Book equation S.2.

\[\Pr[A\mid B]=\frac{\Pr[A\cap B]}{\Pr[B]},\qquad A,B\ \text{independent}\iff \Pr[A\cap B]=\Pr[A]\,\Pr[B].\]

Conditions

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Ledger

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First stated

Primer S section S.1 of Data Mining as Observation, added in draft 0.3 (2026-09-09) for the ECE 514 readers whose first courses are far behind. The idea is standard and TSK Appendix C covers it at length.

Measurements

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Failures and corrections

none

Invariance envelope

none declared

Machine checked

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Used in

Data Mining as Observation primer S.

Related

probability; independence; Bayes' rule; precision, recall; calibration.

See also

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Status

Generated 2026-09-10 by encyclopedia/generate.py; book at observation-data-mining f3914f0; the commit of every record is listed in the encyclopedia’s provenance.

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