Concept

Conditional Probability

Conditional probability updates the sample space after new information is known.

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Concept
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Core
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Reference
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Search Intent
conditional probability

Formula

Conditional probability means the denominator is the new sample space after B is known.

Conditional probability
P(AB)=P(AB)P(B),P(B)>0P(A\mid B)=\frac{P(A\cap B)}{P(B)},\quad P(B)>0

Worked Example

If 4% of policies have a claim and 25% of claim policies are large, then P(large claim)=0.04 x 0.25=0.01, or 1%.

ML Connection

Classification models are often evaluated through conditional probabilities: the chance an event occurs given observed features.

References And Official Sources