Monty hall problem
Hi, it’s been a long time since I posted anything due to a long final exam, and now is my relaxing time. In this blog, I will share a problem that I have just watched from the film “21”: the Monty Hall Problem.
The problem may have been stated:
There are 3 doors: 2 with a goat behind and one with the car behind. At first, you choose, for example, door 1. If the master of ceremonies points to one of the two doors with the goat behind and asks whether you want to change your decision. Would you?
At first, some participants will think of this as a gaslighting trick. But the main character, who set aside his emotions, chose to use statistical math to state his explanation: At first, he had only a 33.3% win, but when the MC chose the goat door and opened it, he believed that his chance was doubled when he changed his decision. At first, I got struggled with how that percentage doubled to 66.6% as it was supposed to be a 50%. A 50/50 situation.
I struggled for a long time till I thought again of the fact that the MC must choose the door with the goat between the two remaining doors apart from your decision. So first among the three options, the participant has a one-third chance of choosing the car. If the chose the car at first and changed her decision, she may lose her care but that chance occurred only one-third of the time. So the chance that she gets her a brand new car will be 66.7%.
