# Conjugate update and MAP

> ML Prep screening item.

- Stable ID: `math-stats-04-beta-posterior-map`
- Collection: screening
- Area: Mathematics
- Topic: Statistics
- Origin: original
- Difficulty: medium
- Expected time: 4 minutes
- Skills: map, bayesian-updating
- Item JSON: https://mlprep.iwase.dev/item/math-stats-04-beta-posterior-map.json

## Problem

A Bernoulli success probability $p$ has prior $\operatorname{Beta}(2,3)$. After
observing $7$ successes and $3$ failures, find the posterior distribution and its MAP.


## 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-stats-04-beta-posterior-map`, and record a real attempt with `recorded_by: "agent"` and `agent_session_id` when available using https://mlprep.iwase.dev/schema/attempt-record.json.