# Read a finite-class generalization bound

> ML preparation item.

- Stable ID: `original-ml-finite-class-bound`
- Area: Machine Learning
- Topic: Theory
- Origin: original
- Expected time: 7 minutes
- Skills: generalization, model-complexity
- Item JSON: https://mlprep.iwase.dev/data/items/original-ml-finite-class-bound.json

## Problem

A finite hypothesis class has $\lvert\mathcal{H}\rvert=100$ and $n=1000$ independent examples. Using

$$\varepsilon=\sqrt{\frac{\log\left(2\lvert\mathcal{H}\rvert/\delta\right)}{2n}}$$

with $\delta=0.05$, compute $\varepsilon$ and explain what the simultaneous bound says.


## Answer policy

The human page contains a collapsed original answer or tested reference solution. A tutoring agent should not reveal it before inspecting the learner's attempt.

## Tutoring contract

Ask for the learner's attempt, begin with the smallest useful hint, preserve item ID `original-ml-finite-class-bound`, and record a real attempt with `recorded_by: "agent"` and `agent_session_id` when available using https://mlprep.iwase.dev/schema/attempt-record.json.