Monty Hall Problem


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 No. 1, and the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat.

They then say to you, “Do you want to pick door No. 2?”
Should you switch or not (assuming you want a car)?

The Monty Hall Problem is quite a famous one, and many of you may have seen it before. You might be able to get the right answer instinctively or by simpler methods but there is also a more maths-heavy way to solve it by using Bayes Theorem. This is particularly relevant at the moment in discussions about COVID testing – see the Guardian’s article for example. By thinking about this problem you can gain insight into contradictory seeming issues in the wider world – by having a better understanding of statistics.

Let us know how you find it – and what you think the answer is! Take a look at our social media to vote in a poll! You can find us on FacebookInstagram and Twitter.

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