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26. Holiday Quiz Show

You're taking part in a quiz where the top prize is a luxury holiday for two. If you answer a simple question correctly - and it is a simple question - then you can choose which one of three boxes to open. One of the three boxes contains air tickets for the holiday of your dreams plus $1000 spending money; the other two are empty.

OK, so you've answered the question correctly and you can now choose which box you'd like - but don't open it yet! Before you open it, the quiz host opens one of the other two boxes to show you that it is empty. She now asks you if you'd like to open the one you chose originally or whether you'd prefer the remaining one.

Should you stick with your original choice or open the other box?
 

Scroll down the page for the answer.


 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

In fact, the best option is to switch from your original choice and open the other box. How do we reach this conclusion?

By choosing one box out of three you had a 1/3 chance of being correct. If, on the other hand, you could have chosen the other two boxes then you would have had a 2/3 chance of winning. Now if you switch from your original choice then that is, in effect, what you are doing and your chances are now 2/3 instead of 1/3 - the quiz host reveals nothing by opening a box and always opens an empty one.
 

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