# Logistic probability and cross-entropy

> ML preparation item.

- Stable ID: `original-ml-logistic`
- Area: Machine Learning
- Topic: Classification
- Origin: original
- Expected time: 6 minutes
- Skills: logistic-regression, cross-entropy, decision-boundary
- Item JSON: https://mlprep.iwase.dev/data/items/original-ml-logistic.json

## Problem

A binary logistic model produces logit $z=\ln(3)$ for a positive example $y=1$. Compute $p(y=1\mid\mathbf{x})$, the predicted class at threshold $0.5$, and binary cross-entropy loss.


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