GATE 2026 DA Q.47: solution and answer

GATE 2026 · DAQ.47 · 2 marks · MSQ

Consider that 20 stories of Author X and 10 stories of Author Y were kept together without mentioning the names of the authors. A classifier was then asked to predict the author (X or Y) of each of these stories. Let, out of X's stories, 6 were classified as that of Y. On the other hand, out of Y's stories, 2 were classified as that of X.

Considering X and Y as two classes, which of the following statements is/are true?

(A)
Accuracy of the classifier is 11/15.
(B)
Precision of Class X is higher than the Precision of Class Y.
(C)
Recall of Class X is higher than the Recall of Class Y.
(D)
Accuracy of the classifier is 14/15.

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Answer and solution

ANSWER

The true statements are (A) and (B).

Official answer: A, BSource: Official answer key, GATE 2026 DA (IIT Guwahati)

Build the confusion matrix. Of the 20 stories by X, 6 were classified as Y, so 14 were classified as X. Of the 10 stories by Y, 2 were classified as X, so 8 were classified as Y.
| | Predicted X | Predicted Y |
|---|---|---|
| Actual X | 14 | 6 |
| Actual Y | 2 | 8 |
Accuracy is the number of correct predictions over the total: $\frac{14 + 8}{30} = \frac{22}{30} = \frac{11}{15}$ . So (A) is true and (D), which claims $\frac{14}{15}$ , is false.
Precision of a class is the fraction of stories predicted as that class that truly belong to it. For X, 14 of the $14 + 2 = 16$ stories predicted as X are correct: $P_{X} = \frac{14}{16} = 0.875$ .
For Y, 8 of the $8 + 6 = 14$ stories predicted as Y are correct: $P_{Y} = \frac{8}{14} \approx 0.571$ . Since $0.875 > 0.571$ , (B) is true.
Recall of a class is the fraction of its actual stories that were found. $R_{X} = \frac{14}{20} = 0.7$ and $R_{Y} = \frac{8}{10} = 0.8$ . Recall of X is lower than recall of Y, so (C) is false.
The true statements are (A) and (B).

KEY IDEA

Build the 2x2 confusion matrix from the counts. Precision divides by the column total (everything predicted as that class); recall divides by the row total (everything that truly is that class); accuracy divides the diagonal by the grand total.

WATCH OUT FOR

Mixing up precision and recall by dividing by the wrong total. Another slip is computing accuracy as 14/15 or from one class only. Here the class with the higher recall (Y) has the lower precision, so swapping the two definitions gives the wrong verdict on (B) and (C).

From the GATE 2026 DA paper. Every question of this paper · Download the full paper · All 2 Bias–variance & CV questions, with notes