Q1. [4] § Case study-based questions
Confusion Matrix for a binary classification model classifying news articles as "Fake News" or "Real News", tested on 500 news articles. The confusion matrix cross-tabulates Predicted vs Reality.
A binary classification model has been developed to classify news articles as either "Fake News" or "Real News". The model was tested on a dataset of 500 news articles, and the resulting confusion matrix is as follows :
- (A) How many total cases are True Negative in the above scenario ? [1]
- (B) Calculate Precision, Recall and F1-Score. [3]
Previously asked in CBSE board exam
2024 104 Q21
Generated by claude-sonnet-4-6 · 2026-06-21 03:18 · grounding stimulus
Model Answer
(A) True Negatives (TN):
True Negative = cases where the model predicted No (Real News) and the reality was also No (Real News).
TN = 420
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(B) Precision, Recall and F1-Score:
From the matrix:
- TP = 45, FP = 15, FN = 20, TN = 420
$$\text{Precision} = \frac{TP}{TP + FP} = \frac{45}{45 + 15} = \frac{45}{60} = \textbf{0.75}$$
$$\text{Recall} = \frac{TP}{TP + FN} = \frac{45}{45 + 20} = \frac{45}{65} \approx \textbf{0.692}$$
$$\text{F1-Score} = \frac{2 \times \text{Precision} \times \text{Recall}}{\text{Precision} + \text{Recall}} = \frac{2 \times 0.75 \times 0.692}{0.75 + 0.692} = \frac{1.038}{1.442} \approx \textbf{0.72}$$
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Explanation
- TN = correctly predicted negatives (Real News predicted as Real News) → 420.
- Precision measures how many predicted "Fake" were actually fake (avoids false alarms).
- Recall measures how many actual "Fake" were correctly caught (avoids misses).
- F1-Score is the harmonic mean of Precision and Recall — useful when classes are imbalanced.
- Always identify TP, FP, FN, TN first before computing metrics; examiners award 1 mark per formula+substitution+result.
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