The Monty Hall Problem

The Monty Hall Problem is a famous probability thought experiment, with a lot of different ways to think about it. It's also a problem where the correct answer is different than the 'intuitive' answer (a bit like the old riddle 'What's lighter; a kilogram of feathers or a kilogram of lead?')

There used to be a game show called Let's Make A Deal hosted by Monty Hall. A common game on the show was this: there were three doors. Behind one door was a car, behind the other two were goats. You/the contestant wanted to pick the car (sorry, goat lovers!) The contestant picks a door at random. Then Monty opens a door. Important things: Monty knows exactly which doors the car and the goats are behind, and the door he opens is:

Then Monty gives you a choice: will you stay with the door you first picked, or switch to the other unopened door?

What strategy would you pick? Stick or switch? Is there a difference in probabilities of winning between the two strategies? Can you prove or show your ideas using maths, a table, or some pictures? When you've worked out what you think, click the link below to find the answer!

The Answer!

(C) Zoe Hills, 2016