# From Accuracy to Precision

*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 III), 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 $N$=1000 objects are given, of which $P$=400 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 Accuracy $= 0.8$. Find the range of possible values of Precision.

**Scoring criterion:** 6 points each for the lower and the upper bound. Total — 12 points

**Maximum score for the task — 12**