# Background Blur Rule

*English translation by SOTA – AI Community of the Russian original. Organisers who would like this translation removed can email sota.ai.community@gmail.com.*

*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, $x$ and $y$, assigning integer scores from 1 to 6. All 36 combinations $(x,\ y)$ are assumed to occur equally often (as when throwing two dice: every combination of faces is equally likely). The camera blurs the background if $x + y \ge 7$. Petya, who does not know $y$, uses a simplified rule: he looks only at $x$ and says “there will be blur” if and only if $x \ge 4$. 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**