Photo Contest: Range of Recall

Photo Contest: Range of Recall

English translation by SOTA – AI Community of the Russian original. Organisers who would like this translation removed can email [email protected].

Task 5 of the school stage of the All-Russian School Olympiad (VsOSh) 2025/26 in artificial intelligence (region group II), grades 9–11. The official answer and solution are in a separate file.

A system that accepts entries for a photo contest marks pictures as suitable (the positive class) or unsuitable (the negative class). A total of $N$=1000 pictures were considered, of which $P$=850 are actually suitable and $N - P = 150$ are unsuitable. Let:

• $TP$ — suitable pictures that the system correctly marked as suitable (True Positives),
• $FP$ — unsuitable pictures mistakenly marked as suitable (false positive detections, False Positives),
• $FN$ — suitable pictures mistakenly marked as unsuitable (False Negatives),
• $TN$ — unsuitable pictures correctly marked as unsuitable (True Negatives).

Metrics:

$$\text{Recall} = \frac{TP}{P},$$

$$\text{Precision (the share of True Positives among all pictures marked as suitable)} = \frac{TP}{TP + FP},$$

It is known that Precision $= 0.8$. Find the range of possible values of Recall. Write the answers as irreducible fractions.

Scoring criterion: 6 points for each correct answer.

Maximum score for the task — 12