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 the stories. Later 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, then which of the following is/are true?

The correct options are:
1. Precision of class X is higher than the precision of class Y.
2. Accuracy of the classifier is 11/15.

Let us analyze the given problem step-by-step to understand why these options are correct.

First, we extract the given information from the problem statement:

Total stories of Author X (Actual Class X): 20
Total stories of Author Y (Actual Class Y): 10
Total number of stories: 20 + 10 = 30

Next, we look at the classifier's predictions:
- Out of X's 20 stories, 6 were classified as Y. This means:
- Stories of X correctly predicted as X (True Positives for X, or TP_X): 20 - 6 = 14
- Stories of X incorrectly predicted as Y (False Negatives for X, or FN_X): 6
- Out of Y's 10 stories, 2 were classified as X. This means:
- Stories of Y correctly predicted as Y (True Positives for Y, or TP_Y): 10 - 2 = 8
- Stories of Y incorrectly predicted as X (False Negatives for Y, or FN_Y): 2

From these classification results, we can construct the confusion matrix:
- True Class X predicted as X (TP_X): 14
- True Class X predicted as Y (FN_X / FP_Y): 6
- True Class Y predicted as X (FN_Y / FP_X): 2
- True Class Y predicted as Y (TP_Y): 8

Now, let us calculate the performance metrics for both classes.

1. Accuracy:
Accuracy is the ratio of correctly predicted observations to the total observations.

$\mathrm{Accuracy}=\frac{{\mathrm{TP}}_X+{\mathrm{TP}}_Y}{\mathrm{Total}}$

$\mathrm{Accuracy}=\frac{14+8}{30}=\frac{22}{30}=\frac{11}{15}$

Thus, the accuracy of the classifier is indeed 11/15, which matches one of the correct options.

2. Precision:
Precision is defined as the ratio of correctly predicted positive observations to the total predicted positive observations for a given class.

For class X:
Total predictions as X = TP_X + FP_X = 14 + 2 = 16

${\mathrm{Precision}}_X=\frac{{\mathrm{TP}}_X}{{\mathrm{TP}}_X+{\mathrm{FP}}_X}=\frac{14}{16}=0.875$

For class Y:
Total predictions as Y = TP_Y + FP_Y = 8 + 6 = 14

${\mathrm{Precision}}_Y=\frac{{\mathrm{TP}}_Y}{{\mathrm{TP}}_Y+{\mathrm{FP}}_Y}=\frac{8}{14}\approx 0.5714$

Comparing the precision values, we have 0.875 > 0.5714, which means the precision of class X is higher than the precision of class Y. This matches the other correct option.