Test your intuition against probability!
Imagine you're on a game show with three doors. Behind one door is a car (🚗), and behind the other two are goats (🐐). You pick a door, then the host (who knows what's behind each door) opens one of the other doors to reveal a goat. Now you have a choice: stick with your original door or switch to the remaining unopened door.
The surprising truth: You should always switch! Switching gives you a 2/3 chance of winning the car, while staying only gives you 1/3.
Initial probabilities:
After the host reveals a goat:
Therefore, switching wins 2/3 of the time, while staying wins only 1/3 of the time.