RunCollection: Simulate chance of matching or beating personal best

Coding: Monte Carlo probability that an in-progress run matches or beats the personal best You are implementing a statistics system for obstacle-course racing. A Course has obstacle_count obstacles. A Run stores the time (seconds) spent on each completed obstacle. A run may be incomplete. A RunCollection stores multiple runs for the same course and can compute the personal best time. Implement in RunCollection: chance_of_personal_best(current_run) -> float Given an in-progress current_run (possibly incomplete), estimate the probability that once completed it will beat or tie the current personal best. Model: For each remaining obstacle i not yet completed in current_run, its completion time is drawn uniformly at random from all recorded times for obstacle i across all other runs in the collection. Incomplete historical runs contribute only the obstacles they actually completed. Simulation: Run 10,000 trials: Sample times for each missing obstacle from its pool. Compute total time for the completed run. Count success if total time <= RunCollection.personal_best(). Return successes / 10,000. Accuracy: The returned value should be consistently within ±0.02 of the true probability. Assumptions: current_run.course == self.course At least one historical run exists. Performance note: Precompute per-obstacle sampling pools to avoid scanning all runs inside each trial. Examples: [[3,3,2],[3,3,3]], current [3,3] => probability 1/2. [[3,3,2,3],[3,3,3,2],[5,5,2]], current [3,3] => probability 5/6. Constraints: obstacle_count: 1..10,000 number of runs: 1..10,000 trials: 10,000 Example Input # Example 1 course_obstacles=3 runs=[[3,3,2],[3,3,3]] current=[3,3] Output ~0.50 (value should be in [0.48, 0.52])