# Count a union of selection events

> ML Prep screening item.

- Stable ID: `math-prob-01-counting-events`
- Collection: screening
- Area: Mathematics
- Topic: Probability
- Origin: original
- Difficulty: easy
- Expected time: 3 minutes
- Skills: counting, event-algebra, inclusion-exclusion
- Item JSON: https://mlprep.iwase.dev/item/math-prob-01-counting-events.json

## Problem

Two people are chosen uniformly from five people, including Ana and Ben. Let
$A$ be the event that Ana is chosen and $B$ the event that Ben is chosen.
Compute $P(A)$, $P(B)$, $P(A\cap B)$, $P(A\cup B)$, and $P(A^c\cap B^c)$.


## 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-01-counting-events`, and record a real attempt with `recorded_by: "agent"` and `agent_session_id` when available using https://mlprep.iwase.dev/schema/attempt-record.json.