# Cost-sensitive threshold

> ML Prep screening item.

- Stable ID: `ml-screen-classification-advanced-cost-threshold`
- Collection: screening
- Area: Machine Learning
- Topic: Classification
- Origin: original
- Difficulty: hard
- Expected time: 10 minutes
- Skills: cross-entropy, classification-thresholds
- Item JSON: https://mlprep.iwase.dev/item/ml-screen-classification-advanced-cost-threshold.json

## Problem

A calibrated classifier outputs $p=P(y=1\mid x)$. A false positive costs $1$, a false negative costs $4$, and correct decisions cost $0$. Derive the threshold for predicting $1$. With ties assigned to class $1$, classify $p=(0.1,0.2,0.7)$. If the labels are $(0,1,0)$, compute mean 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-advanced-cost-threshold`, and record a real attempt with `recorded_by: "agent"` and `agent_session_id` when available using https://mlprep.iwase.dev/schema/attempt-record.json.