Question

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.

Hint:

Build the 2x2 confusion matrix from the story counts first (14, 6, 2, 8), then compute accuracy, precision per class, and recall per class from it.

Answer 1

The Correct Option is A, B

The classifier makes two kinds of errors: 6 of X's 20 stories are wrongly tagged Y, and 2 of Y's 10 stories are wrongly tagged X. That means, out of 30 stories in total, 14 X-stories and 8 Y-stories are labeled correctly, and the remaining 8 stories (6 + 2) are labeled wrong. Let's check each statement in turn.

1. Accuracy is 11/15: Accuracy counts every correct call over every story: $(14+8)/30 = 22/30$. Dividing top and bottom by 2 gives $11/15$. This statement is true.
2. Precision of X is higher than Precision of Y: Precision asks, out of everything the classifier called a given class, how much of it was actually that class. The classifier called 16 stories "X" in total (14 real X plus 2 real Y mislabeled), and 14 of those really were X, giving $14/16 = 0.875$. It called 14 stories "Y" in total (8 real Y plus 6 real X mislabeled), and 8 of those really were Y, giving $8/14 \approx 0.571$. Since $0.875 > 0.571$, this statement is true.
3. Recall of X is higher than Recall of Y: Recall asks, out of every story that truly belongs to a class, how much did the classifier catch. For X, 14 out of the 20 real X stories were caught: $14/20 = 0.7$. For Y, 8 out of the 10 real Y stories were caught: $8/10 = 0.8$. Since $0.7 < 0.8$, X's recall is lower, not higher, so this statement is false.
4. Accuracy is 14/15: We already found the true accuracy is $11/15$, which is about $0.733$, not $14/15 \approx 0.933$. This statement is false.

So the true statements are the first two: the accuracy is 11/15, and X's precision beats Y's precision. The apparent asymmetry, X has better precision but worse recall than Y, happens because Y has fewer stories overall (10 vs 20), so the 2 misclassified Y stories hurt Y's precision more than they hurt X's recall.

Let's summarize:

• Accuracy = 22/30 = 11/15, matching statement (A).
• Precision$_X$ = 14/16 = 0.875 is greater than Precision$_Y$ = 8/14 ≈ 0.571, matching statement (B).
• Recall$_X$ = 0.7 is less than Recall$_Y$ = 0.8, so statement (C) fails.

The correct choices are (A) and (B).