Precision and recall are exact rational rates formed from the operating-point counts. This lesson shows the trade-off on discrete thresholds, with no smooth curve implied.
highlighted = computed this step
Precision and recall
Each operating point has exact rational rates. At threshold 5, precision is 1 and recall is 1/3. At threshold 1, precision is 3/5 and recall is 1. Both rates are recomputed from the visible counts, so every numerator and denominator stays attached.
P,R∈{(1,1/3),(3/5,1)}
The trade-off
Lowering the threshold catches more positives, so recall rises from 1/3 to 1. It also admits more false positives, so precision falls from 1 to 3/5. The trade-off is measured at exact listed thresholds, not smoothed into a hidden continuum.
R↑,P↓
Summary
The table is the curve discipline: discrete exact points, no smooth continuum. A line between points would be only a visual guide, not a claim about intermediate thresholds.