Implement chance of a personal best

You are given a simplified model for tracking race times on an obstacle course. - A **course** has a fixed number of obstacles. - A **run** records the time spent on each obstacle in order. - A run may be **complete** or **incomplete**. - A **run collection** stores many runs for the same course. For an obstacle index `i`, the historical times available for that obstacle come from **all other runs that reached obstacle `i`**, including incomplete runs. Implement the method `chance_of_personal_best(run)` in `RunCollection`. ### Required behavior Given an **in-progress** run: 1. Perform **10,000 simulation trials**. 2. In each trial, for every obstacle not yet completed in the current run, randomly choose one historical time for that obstacle from the other runs in the collection that have a recorded time for that obstacle. 3. Combine the current run's existing obstacle times with the sampled remaining times. 4. Check whether the simulated total time is **less than or equal to** the current **personal best**. 5. Return the fraction of trials that are a personal best (or tie the personal best). ### Important details - The current personal best is the **minimum total time among completed runs only**. - When sampling future obstacle times, include times from incomplete historical runs **if they reached that obstacle**. - Do **not** sample from the in-progress run being evaluated. - The returned value should be a floating-point probability, and with 10,000 trials it should usually be within **0.02** of the true probability. ### Example Suppose a course has 3 obstacles and the historical runs are: - `[3, 3, 2]` - `[3, 3, 3]` The current in-progress run is `[3, 3]`. The personal best among completed runs is `8`. For the last obstacle, the historical times are `{2, 3}`. So the simulated completed run is either `[3,3,2]` or `[3,3,3]`, each with equal probability. Therefore the chance of matching or beating the personal best is about `0.5`. ### Starter structure Assume classes similar to the following already exist: - `Course(title, obstacle_count)` - `Run(course)` with fields: - `course` - `complete` - `obstacle_times` - `add_obstacle_time(t)` - `get_run_time()` - `RunCollection(course)` with field: - `runs` Write the `chance_of_personal_best` method for `RunCollection`.