Restricted Probability Space

Definition

Restricted Probability Space in plain English

Pull Restricted Probability Space when the sample space is conditional or reduced by a prior filter. Clues include given that, among those who, or conditional probability. Rebuild the denominator as the restricted set first; only then count the numerator inside it. Using the unrestricted denominator quietly answers a different question than the one asked. Say the given clause out loud so the new sample space is explicit before any fraction is written. Micro-example: 100 students, 40 in choir, 10 in choir and band. P(band mid choir) uses denominator 40, not 100, so 10/40 = 1/4. A common trap is computing P(A and B)/P(total) instead of P(A and B)/P(B); the given clause chooses the denominator.

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