Checklist VsOSh AI 2026 School Stage (Sirius platform, region group 2), grades 9–11 · Task 2
Forecasting Ball Colours
Russian title: Задание 2
Compute the expected number of correct predictions when always predicting the less likely colour.
The task
Every minute a machine independently releases a red ball with probability 2/3 or a blue ball with probability 1/3. Before the contest participants saw the last six balls: blue, red, blue, blue, red, blue. Vasya noticed that blue appeared more often and predicted "blue" for each of the next three minutes.
Find the expected number of his correct predictions over the next three minutes.
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
Forecasting Ball Colours
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 II), grades 9–11. The official answer and solution are in a separate file.
An artificial intelligence club is holding a forecasting contest. There is a machine: every minute it produces a ball — either red with probability or blue with probability . This happens independently: the colour of one ball does not affect the colour of the others. Before the contest began, the participants were told in what order the balls had come out over the last six minutes:
According to the rules, three fields — the predictions for the next three minutes — must be filled in in advance and the sheet handed in. Vasya noticed that blue had occurred more often and wrote “blue” in all 3 fields. Find the mathematical expectation of the number of Vasya's correct predictions over the next three minutes, that is, how many of these three predictions will turn out to be correct on average?
Scoring criterion: exact match of the answer — 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 II, 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
- One number.
- Scoring
- Exact answer; 12 points.
- Format
- School stage on the Sirius.Courses platform, region group 2, 24 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).