First prize is a used handkerchief

I’m not going to lie, my past few weeks have been largely unproductive and uneventful. The majority, if not all off my time has quite literally been taken up marking student essays and reports. It is an incredibly boring, tedious and painful exercise and I do not wish to reminisce on the experience here. Instead I thought I’d present a statistics puzzle that I just gave to my first year statistics class and that I find very cool.

Suppose you’re on a game show and you’re given the choice to pick one of three doors. Behind each door is the prize that you’ll win. Behind one door is an infinitely cool prize (insert an infinitely cool prize of your choice), behind the other two doors are foils or dud prizes, lets say someone’s used handkerchief (not much fun). It is important to know that the host of the game show knows what is behind each door.

So lets say you pick door number 1. Before they tell you what you've won, the host then opens door number 3 and reveals a used handkerchief. The host then says to you, “Would you like to change your choice to door number 2 or stick with your original choice of door number 1?”

The question is, given the new information provided to you that door number 3 did not contain the infinitely cool prize, should you change your decision and pick door number 2, stick with your original choice of door number 1 or does it make no difference either way?

Anyway have a think about it and I'll post the answer this time next week. If you know the answer please resist from posting it in the comments section. First person to email me the correct answer though will win one of my very own used handkerchiefs. Get to it!

James

jdretell@gmail.com

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