A sample space is the set of all possible outcomes or events in a random experiment or situation. Conditional information narrows this set, changing the denominator used to calculate probability and often changing the resulting decision. section 3.3 section 3.4
Use a restricted sample space to interpret probability after new information becomes available:
- Weather: narrow all weather conditions to cloudy and rainy conditions after observing dark clouds or nearby rain. section 3.3.1
- Medical testing: restrict the population to people with positive test results before assessing disease probability. section 3.3.1
- Traffic, sports, and investment decisions: condition on an accident, an injured player, or recent market information. section 3.3.1
Contingency-table calculation
A table records symptoms and test results. Among the 50 people with symptoms, 40 test positive, giving 40/(40+10) = 80%. Among the 130 people with positive tests, 40 have symptoms, giving 40/(90+40) ≈ 30.77%. The numerator stays the same while the selected sample space changes. section 3.3.3
