一个订阅，多种模型，共享额度。

Result: precision is 80%; recall is 60%.

1. Reconstruct the confusion matrix
True positives: 12 spam messages flagged correctly.
False positives: 3 legitimate messages flagged incorrectly.
False negatives: 20 − 12 = 8 spam messages missed.
True negatives: 80 − 3 = 77 legitimate messages left alone.
Check: 12 + 3 + 8 + 77 = 100 messages.

2. Calculate the metrics
Precision = TP / (TP + FP) = 12 / 15 = 0.80.
Recall = TP / (TP + FN) = 12 / 20 = 0.60.
F1 = 2 × precision × recall / (precision + recall) = 0.686, approximately 68.6%.
Accuracy = (12 + 77) / 100 = 89%. High accuracy alone hides the eight missed spam messages.

3. Interpret the trade-off
Of the flagged messages, one in five is legitimate. Of all spam messages, two in five are missed. Raising the decision threshold may reduce false positives while missing more spam; this is a tendency to measure, not a guaranteed outcome.

4. Recommended next step
Use a held-out, representative labelled sample and compare precision-recall curves across thresholds. If flags delete messages automatically, review false positives carefully. If flags only route to human review, evaluate review capacity and the cost of missed spam before choosing a threshold.

Limit: these 100 fictional examples do not establish production performance or statistical confidence. Retain the labels and threshold in the evaluation record.