The Monty Hall problem

The Monty Hall problem is another problem from our new problem book:

Book Pic

This problem has an amazing history which you can look up on line, as well as the strange property of making some people really angry. In fact, it makes some people so angry that it probably best to never talk about this problem with anyone ๐Ÿ™‚ I broke that rule today.

Here’s a fairly typical statement of the problem, from Wikipedia’s entry on the 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. He then says to you, “Do you want to pick door No. 2?” Is it to your advantage to switch your choice?”

For the project today my goal was pretty simple: (1) Have the boys talk about their initial reactions to the problem, and (2) Have them see that the outcomes from the “switching” and “not switching” strategies are different.

So, their initial reaction:

 

Next up, walking through the “switching” strategy:

 

Now we compare to the “don’t switch” strategy:

 

Finally – what’s going on in this problem?? Walking through the problem with clear cups seemed to help them understand why the switching and not switching strategies were different:

 

So, a fun project talking through a famous (and perhaps infamous) probability problem. A neat problem for kids and definitely a fun classroom activity. Watch out for making people really angry, though (seriously)!

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Comments

3 Comments so far. Leave a comment below.
  1. I’d just point out that Jason Rosenhouse’s 2009 volume, “The Monty Hall Problem” is a fantastic source for covering the many different permutations/variations/aspects of MHP. Plenty of other books cover it, as well as many websites, but I think Rosenhouse does the best job.

  2. Also, there are a number of interactive Monty Hall simulation sites on the Web that the boys, or any intrigued adults ๐Ÿ˜‰ can have fun playing (and confirming what you’ve shown). Here’s one:
    http://montyhallpuzzle.appspot.com/

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