# Probability Threshold

*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 6 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.*

The data for this task are in a spreadsheet file. You can download the file in one of three formats: XLSX, ODS, CSV.

In the document, each row contains two numbers:

- the probability of a positive outcome $p$ (a number from 0 to 1);
- the correct label $y$, where $y = 1$ is a positive outcome and $y = 0$ is a negative one.

Let us define a simple prediction rule:

$$\hat{y} = \begin{cases} 1, & \text{if } p \ge 0.6, \\ 0, & \text{if } p < 0.6. \end{cases}$$

**Problem.** Find the number of rows for which the prediction $\hat{y}$ coincides with the correct label $y$.

**Scoring criterion:** exact match of the numerical answer — 12 points

**Maximum score for the task — 12**