conditional probability concept
| Definition | The 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. |
|---|---|
| Example | Given that the first die shows three, the sum is seven only when the second shows four, probability one sixth. |
| Book | Data Mining as Observation, draft 0.2, commit f3914f0; entry id conditional-probability, kind concept. |
| Status | no ledger row names this entry. Corrections: none recorded. |
| Defining equation | Book equation S.2. |
| Assumptions and scope | none |
| Prior art | none recorded |
| Evidence | none |
| Reviewed | semantic 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
none
Ledger
none
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
none
Failures and corrections
none
Invariance envelope
none declared
Machine checked
none
Used in
Data Mining as Observation primer S.
Related
probability; independence; Bayes' rule; precision, recall; calibration.
See also
none
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.