You're at a Tampa Bay Rays baseball game, soaking in the atmosphere. Unexpectedly, you're announced as the $20$ millionth visitor! Confetti showers down, and you're presented with season tickets and the promise of free hotdogs at every game. The excitement is palpable.

Yet, amidst the celebrations, a thought strikes you. Given the sheer number of spectators over the years, there's a statistical likelihood of injuries from foul balls.

Drawing upon Heinrich$$s Accident Pyramid, you ponder: With $20$ million patrons attending games, what's the projected number of hospitalizations due to foul ball injuries, assuming the hazard has been mitigated?