Monty_Hall_Probabilities
The Monty Hall problem is a brain teaser, in the form of a probability puzzle, loosely based on the American television game show Let’s Make a Deal.
Suppose you’re on a game show, and you’re given the choice of three doors. Behind one door is a car; behind the others, goats. You pick a door, say number 1, and the host, who knows what’s behind the doors, opens another door, say number 3, which has a goat. He then says to you, “Do you want to pick door number 2?”
Is it to your advantage to switch your choice?
It turns out that the probabilities of the contestant to win if he changes the door is the double vs not to change, roughly 67% and 33% chance respectively.
This case study will prove this converging probabilities in the long run (long number of trials) through random experiments, comparing the outcome (winning cases) of changing or not the door.