Almost Everyone Gets This Question Wrong

I came across an interesting problem yesterday. It seems simple but almost everyone gets it wrong:

You’re on a game show. The host shows you three doors. Behind one is a car. Behind the other two, nothing. Choose correctly and a brand new car is yours!

You choose Door #1. The host opens Door #2 and shows you there’s nothing behind it. He then gives you a choice: stay with Door #1, or switch to Door #3.

Which should you choose?

What most people, including me, think at first is that it doesn’t matter. You could either switch or stay with Door #1. Either way you’d have a 50/50 shot.

Most people are wrong. You actually have a 2/3rds chance of winning that awesome new car if you switch to Door #3!

But how can that be? You’ve got two possibilities, so that’s 50/50 odds right? The key is that the game show host already opened Door #2.

Before he did that, there was a 2/3rds chance that the car was behind either Door #2 or Door #3. After he opens Door #2 and shows you there’s nothing there, that’s still true. There is a 2/3rds chance it’s behind Door #2 or Door #3, except now Door #2 is eliminated. So there’s a 2/3rds chance that the shiny new car is behind Door #3, and you should switch.

This is called the Monty Hall Problem, and if you got it wrong, you’re in good company. Mathematicians and even the brilliant professor who’s teaching the class I’m taking got it wrong at first.

I find this problem fascinating because it shows us how wrong our intuitions can be, even in simple circumstances like these. If you’re interested in more puzzles like this, you can sign up for the Puzzles, Problems and Paradoxes class here. It’s online every Wednesday at 11:10am Central through UT-Austin. You’ll have missed the first of six classes, but believe me, it’ll still be worth your $108. The professor was one of my favorites from college and it’s a privilege to be able to learn again from this brilliant man!

For more posts on philosophy and the mind, check these out:

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