Why Machines Learn: The Elegant Math Behind Modern AI

by Anil Ananthaswamy

“Suppose you are on a game show, and you’re given the choice of three doors. Behind one is a car; behind the others, goats. You pick a door, say, No. 1, and the host, who knows what’s behind the doors, opens another door, say, No. 3, which has a goat. He then says to you, ‘Do you want to pick No. 2?’ Is it to your advantage to switch your choice?” The person playing the game has a quandary. Do they switch their choice from door No. 1 to door No. 2? Is there any benefit to doing so, in that they will increase their odds of choosing the door hiding the car? Before we look at vos Savant’s answer, let’s try to tackle the problem ourselves. Here’s my intuitive answer: Before the host opens one of the doors, the probability that a car is behind the door I’ve picked (Door No. 1) is one-third. But then the host opens Door No. 3 and reveals that there’s a goat behind it. Now there are two closed doors, and behind one of them is the car. I figure that the car is equally likely to be behind one or the other door. There’s no reason to switch my choice.