推荐系统的预测结果与真实结果的相关性统计如下表所示：

The correlation statistics between the predicted results of the recommender system and the real results are shown in the following table:

选中selected 未选中unselected total
相关related 4 2 6
不想关unrelated 3 1 4
total 7 3 10

请计算准确率

Please calculate the P

Question

推荐系统的预测结果与真实结果的相关性统计如下表所示：

The correlation statistics between the predicted results of the recommender system and the real results are shown in the following table:

选中selected	未选中unselected	total
相关related 	4	2	6
不想关unrelated	3	1	4
total	7	3	10

请计算准确率

Please calculate the P

BlackTom AI · Accepted Answer

Precision P (准确率) measures the fraction of predicted positives that are actually positive: P = true positives / (true positives + false positives).

Relevant knowledge:
- Interpret the contingency table as a confusion matrix where columns are predictions (selected = predicted positive, unselected = predicted negative) and rows are actual labels (related = actual positive, unrelated = actual negative).
- True Positive (TP): predicted selected and actually related.
- False Positive (FP): predicted selected but actually unrelated.
- Precision P = TP / (TP + FP).

Step-by-step reasoning with all intermediate steps:
1. Read the table and label cells:
   - Actual related & predicted selected = 4 → TP = 4.
   - Actual unrelated & predicted selected = 3 → FP = 3.
   - Actual related & predicted unselected = 2 → false negatives (FN) = 2 (used for recall, not precision).
   - Actual unrelated & predicted unselected = 1 → true negatives (TN) = 1.
2. Compute the denominator (predicted positives): TP + FP = 4 + 3 = 7.
3. Compute precision: P = TP / (TP + FP) = 4 / 7.
4. Optionally as decimal: 4/7 ≈ 0.5714 (57.14%).

Why 4/7 is correct:
- Precision asks: of the 7 items the system predicted as “selected”, how many were actually “related”? That count is 4 out of 7, so precision = 4/7.

Why the other choices are incorrect:
- 2/3 equals 4/6 and corresponds to recall (TP / (TP + FN) = 4 / (4 + 2)), not precision.
- 8/13 has no correct mapping to standard measures from these counts; the total is 10, so 8/13 is unrelated to TP, FP, TN, FN here.
- 2/5 (0.4) does not match any standard ratio from the table (specificity = TN/(TN+FP) = 1/(1+3) = 1/4, not 2/5).

Conclusion: The precision P = 4/7, which matches the provided correct answer.

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