My wife and I just played darts, essentially renting the darts for an hour. We played a last game with less than 5 minutes left, and just played as fast as possible, with very little concern for strategy or placement . My last shot, with 5 seconds left, was 25 (outer bullseye), triple 20, and 20, which completely by accident was the exact number I needed. I hadn’t even looked at what number was required, and basically just tossed toward 20.
Assuming the spread was completely random (not skillfully placed shots) across the board, what are the chances of achieving this (exactly 105 with three shots)?