# State the LLN operationally

> ML Prep screening item.

- Stable ID: `math-prob-08-lln-interpretation`
- Collection: screening
- Area: Mathematics
- Topic: Probability
- Origin: original
- Difficulty: easy
- Expected time: 2 minutes
- Skills: law-of-large-numbers
- Item JSON: https://mlprep.iwase.dev/item/math-prob-08-lln-interpretation.json

## Problem

If $X_1,X_2,\ldots$ are i.i.d. $\operatorname{Bernoulli}(0.3)$ and
$\bar X_n=n^{-1}\sum_iX_i$, state the weak law of large numbers for this case.
What does it imply about $P(|\bar X_n-0.3|>0.05)$ as $n\to\infty$?


## Answer policy

The human page contains a collapsed answer. 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 `math-prob-08-lln-interpretation`, and record a real attempt with `recorded_by: "agent"` and `agent_session_id` when available using https://mlprep.iwase.dev/schema/attempt-record.json.