Debug and extend obstacle-run statistics classes

## Problem: Obstacle course run statistics (debug + implement) You are building software to track how long racers take to complete an obstacle course. ### Domain model - A **Course** has: - `title` (string) - `obstacle_count` (int): number of obstacles in the course - A **Run** represents one attempt on a Course: - `obstacle_times`: list of per-obstacle completion times (seconds) - `complete`: boolean that becomes `True` when `len(obstacle_times) == course.obstacle_count` - `add_obstacle_time(t)`: appends a time for the next obstacle; throws if run is already complete - `get_run_time()`: sum of the recorded times so far (for incomplete runs, sum of completed obstacles) - A **RunCollection** stores many runs for the *same* course: - `add_run(run)`: adds a Run; rejects runs from a different Course - `personal_best()`: the minimum total time among **complete** runs ### Tasks 1. **Debugging:** - There is a bug in the provided `RunCollection` implementation that causes an existing unit test to fail. - Fix `RunCollection` so that the provided test suite passes. 2. **Implement `best_of_bests()` in `RunCollection`:** - Definition: the fastest possible run time if everything went perfectly. - Compute it by taking, for each obstacle index `i`, the minimum observed time for obstacle `i` across **all runs** that reached that obstacle (including incomplete runs), and summing these per-obstacle minima. - Add (or update) a unit test verifying correctness. 3. **Implement `chance_of_personal_best(test_run)` using simulation:** - Input: an **in-progress** `Run` (may have completed some obstacles but not all). - Assume that for each remaining obstacle `i` not yet completed in `test_run`, the time to complete obstacle `i` is drawn **uniformly at random** from the set of historical times recorded for obstacle `i` in the run collection (including obstacle times from incomplete runs, as long as that obstacle time exists). - Run **10,000 trials**: - For each trial, sample times for the missing obstacles and add them to `test_run`’s current elapsed time. - Count the fraction of trials where the completed simulated total time is **<=** the current `personal_best()`. - Return that fraction as a float. - Accuracy requirement: the returned value should be within **±0.02** of the true probability. 4. **Testing & code quality discussion:** - What additional tests would you add (beyond the provided ones)? - After implementing `best_of_bests()` and `chance_of_personal_best()`, what improvements would you make to the codebase (structure, naming, performance, reliability, determinism of tests, etc.)? ### Notes / edge cases to consider - Some runs may be incomplete. - `personal_best()` is defined only over complete runs. - The run collection is assumed to contain runs for exactly one course. - Sampling for obstacle `i` requires there to be at least one historical time recorded for that obstacle.