This is based on the game show "Let's Make a Deal." There are 3 doors. Behind 2 of them is a goat, behind the other is a car. The host asks you to pick a door. You win whatever is behind the door you pick. (Assume you want a car and not a goat).
The host then reveals what is behind one of the doors that you did not choose. The host will always show you that behind one of those doors is a goat (because where would the drama be if they showed you a car and you automatically lost?).
The host then asks you, what do you want to do now? Switch your door or stay with the door you've chosen?
Most people are absolutely CONVINCED that there is no reason to switch doors, and there is still an equal probability (of having a car) between the door you chose and the one remaining door.
This is not true. You are actually twice as likely to get the car by switching doors. This can be shown mathematically with the Bayes theorem.
More intuitively, since there are 2 goats and 1 car, we can analyze the probabilities based on your initial choice:
If your door had a goat (with 2/3 probability) and you switch you have a 100% (=1) chance of getting a car, since you now know one of the doors you didn't pick has a goat. The probability that you get a car when you switch is (2/3)*1 = (2/3).
If your door had a car (with 1/3 probability) and you do not switch, you have a 100% probability of winning the car, so you have a (1/3)*1 chance of winning the car.
So the probability of getting a car by switching is 2/3 and the probability of getting a car by not switching is 1/3.
TL;DR: If you're ever on "Let's Make a Deal", ALWAYS choose to switch your door Proof