The Monty Hall Problem: It’s a Piece of Cake

October 31, 2021 by · Comments Off on The Monty Hall Problem: It’s a Piece of Cake 

In chapter 1 of Harvard psychology professor Steven Pinker’s new book, Rationality: What It Is, Why It Seems Scarce, Why It Matters, Pinker discusses the so-called “Monty Hall problem”, which concerns the tricky probabilities involved in a game-show that is similar to the old TV game show “Let’s Make a Deal”.  In the game, there are three numbered doors, and a prize exists behind only one of the doors. The player chooses one of three numbered doors. Game host Monty Hall – who knows behind which of the three doors there is a prize – then eliminates one of the two remaining doors. However, the rules of the game do not allow Monty to eliminate a door having a prize behind it. Monty then asks the player whether she would like to trade her door for the one remaining door.

The Monty Hall problem asks: To maximize her chance of winning the prize, should the player trade her door for the remaining door?  Interestingly, according to Pinker, most people answer that there is no point in switching doors because – there being only two doors left – the prize is just as likely to be behind one door as it is to be behind the other remaining door (i.e., there is a 50/50 chance of choosing correctly). However, the mathematically correct answer to the question is that the player should trade her door for the other remaining door, because there is a 2/3rds chance that the prize is behind the door Monty did not eliminate, and their remains only a 1/3rd chance that the prize is behind the door initially chosen by the player. Read more