# Logistic probability and loss

> ML Prep screening item.

- Stable ID: `ml-screen-classification-foundation-logistic`
- Collection: screening
- Area: Machine Learning
- Topic: Classification
- Origin: original
- Difficulty: easy
- Expected time: 5 minutes
- Skills: logistic-regression, cross-entropy, decision-boundary, classification-thresholds
- Item JSON: https://mlprep.iwase.dev/item/ml-screen-classification-foundation-logistic.json

## Problem

A binary logistic model has logit $z=w_1x_1+w_2x_2+b$. State its feature-space decision boundary at threshold $0.5$. Then, for an example with $z=\ln 4$ and $y=0$, compute $P(y=1\mid x)$, the predicted class, and binary cross-entropy.


## 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 `ml-screen-classification-foundation-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.