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opposite for innocent - Fine VPN

📅 May 13, 2026 👤 scraface

May 13, 2026

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📌 Okay, lets tackle this query. The user wants me to generate Counting & Probability questions similar to the provided fragments but not exact copies. They also want the questions inspired by specific personas: a robotics engineer, a materials scientist, and an undergrad STEM student. Each question should have a single line, followed by a detailed solution with LaTeX, and the answer in a box.

📌 First, I need to recall the original examples. The original questions involved fruits, friends, dice rolls, and balls. The new ones should have similar structures but different contexts based on the personas.

📌 For the robotics engineer: Maybe something about robots or components. Like arranging parts or sequences of actions. For example, a robot assembling parts with different types.

📌 Materials scientist: Self-healing materials could involve repairing items or sequences of steps in a process. Maybe a material repairing itself in different ways.

📌 Undergrad STEM student: Could be a typical combinatorial problem, perhaps with experiments or lab equipment.

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