Friday, July 24, 2009

Let's Make a Deal!

When I began this blog, it was my intention to write about interesting facts or consumer trends I encounter in my life as a nerdling. But as I review my blogs to date I must take note of the fact that all my stories are about my own experiences. Grant it, my life has provided plenty of material over the past few weeks, but it’s time to get back to my original intent.

A couple months ago, one of my co-nerdlings came into my office with a puzzle. Here’s the gist of what he said.

Say you’re on the game show Let’s Make a Deal and Monty Hall asks you to pick 1 of 3 doors. Behind one door is a car; behind the other 2 cars are goats. After you make your pick Monty opens up one of the doors you didn’t pick and there’s a goat behind it. He then asks you if you would like to change your door or stick with your 1st choice. What should you do?

My immediate answer was: "It doesn’t matter. There’s a 50-50 chance that the car is behind the door I picked.”

Jeff said, “Are you sure?”

I said, “Of course I’m sure! It’s either the one I picked or the other one. That’s 50-50!”

Jeff: “Are you positive?”

Lou: “Yes!”

Jeff: “Want to make a wager?”

Self doubt begins to set in, considering Jeff is a complete genius. So I decided to draw all the possible scenarios and corresponding outcomes on a sheet of paper.

Assume that the car is behind door A. There are 3 possible scenarios:

1. I correctly choose door A and Monty opens one of the other doors (B or C)
2. I incorrectly choose door B and Monty opens door C (he’d never open door A)
3. I incorrectly choose door C and Monty opens door B

If I stuck with my original guess I would have a 1/3 chance of being correct (scenario 1). If I changed my original guess, I would have a 2/3 chance of being correct (I would chose door A in both scenarios 2 and 3.)

So, by switching I’d actually increase my odds to 2 out of 3.

Man! I guess I failed that test!

There is a name for this brain twister – it’s the Monte Hall problem. Even PhD mathematicians get the problem wrong (which makes me feel a bit better).

Now all I have to do is get on Let’s Make a Deal so I can win a car. But with my luck I’ll come home with a goat.

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