Checklist VsOSh AI 2026 School Stage (Sirius platform, region group 4), grades 9–11 · Task 2
Background Blur Rule
Russian title: Задание 2
Find the probability that a simplified threshold rule agrees with a camera's blur decision.
The task
A camera scores each photo with integers x and y from 1 to 6, all 36 combinations being equally likely, and blurs the background if x + y ≥ 7. Petya, not knowing y, predicts blur if and only if x ≥ 4.
With what probability does Petya's answer match the camera's decision for a random photo?
Abridged and translated by SOTA from the official Russian materials. The official statement has the exact rules, and it wins wherever this summary differs.
In English
This task was published in Russian. SOTA translated its 3 files into English on 16 September 2026.
- Task statement Russian original of Task statement
- Official solution Russian original of Official solution
- Full paper with solutions (all tasks of the tour) Russian original of Full paper with solutions (all tasks of the tour)
Read the task statement in English
Background Blur Rule
English translation by SOTA – AI Community of the Russian original. Organisers who would like this translation removed can email [email protected].
Task 2 of the school stage of the All-Russian School Olympiad (VsOSh) 2025/26 in artificial intelligence (region group IV), grades 9–11. The official answer and solution are in a separate file.
In automatic camera mode, a smartphone rates every image on two parameters, and , assigning integer scores from 1 to 6. All 36 combinations are assumed to occur equally often (as when throwing two dice: every combination of faces is equally likely). The camera blurs the background if . Petya, who does not know , uses a simplified rule: he looks only at and says “there will be blur” if and only if . What is the probability that Petya's answer coincides with the smartphone's decision for a randomly chosen photo?
Scoring criterion: 6 points for each correct answer. Total — 12 points
Maximum score for the task — 12
Translated by SOTA. The Russian original is the official version and wins wherever the two differ. Statement and official solution come from one PDF, the analysis of the school-stage tasks for region group IV, grades 9–11, linked from the olympiad's Sirius page. If you organise this olympiad and would like the translation removed, email [email protected] and we will take it down.
At a glance
- You get
- Statement only.
- You submit
- A probability (fraction).
- Scoring
- Exact answer; 12 points (the PDF describes the criterion as "6 points per correct answer, 12 in total").
- Format
- School stage on the Sirius.Courses platform, region group 4, 21 October 2025; grades 9–11; individual; 150 minutes; maximum 112 points for the paper (tasks 1–6: 12 points each; tasks 7–8: 20 points each).