# From Precision to Accuracy

*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 5 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 a binary classification problem (dividing objects into 2 classes), a total of $N$=800 objects are given, of which $P$=200 are positive and $N - P = 600$ are negative. Let:

- $TP$ — correctly predicted positive objects (True Positives);
- $FP$ — negative objects mistakenly predicted as positive (False Positives);
- $FN$ — positive objects mistakenly predicted as negative (False Negatives);
- $TN$ — correctly predicted negative objects (True Negatives).

Metrics:

$$\text{Precision (precision for the positive class)} = \frac{TP}{TP + FP},$$

$$\text{Accuracy (the share of correct answers)} = \frac{TP + TN}{N},$$

It is known that Precision $= 0.5$. Find the range of possible values of Accuracy.

**Scoring criterion:** each of the two numbers is worth 6 points; maximum 12 points.

**Maximum score for the task — 12**