Yet Another Math Problem

AlmostAtheist

This is a popular one, and I'm intentionally rewording it in the hopes that it can't be easily google'd. (Hopefully I won't also screw it up!)

Let's say I'm in a generous mood, and I invite you to choose from three cardboard boxes in my living room. You can't touch them, and they are identical. One of them contains $100,000 in cash, the other two are empty.

Left with no way to tell one from another, you randomly select one.

Still feeling generous, I decide to give you a break. I open one of the boxes you did NOT choose and show you that it is empty. I now give you the chance to change your answer and select the remaining unopened box.

What should you do? Keep your original decision? Switch? Or does it matter one way or the other?

Dave

LittleToe

Switch.

Statistically the probability is that the other one is 3x as likely to hold the cash.

crazyblondeb

I knock you over, and grabb both boxes!!

DJK

I would stay with my first choice. I have never been given a second chance if I was right the first time. It doesn't make sense.

sir82

Switch.

It is counterintuitive, but the laws of probablility dictate that your odds of winning are greater if you switch. I don't recall the details of how the math works.

LittleToe

A grasp of counter-intuition can be the basis of good spirituality. This is why the "Hanged-Man" card in the Tarot deck is so representative of that part of the journey of life. Pascal's wager is based on a simlar concept

AlmostAtheist

>>It is counterintuitive, but the laws of probablility dictate that your odds of winning are greater if you switch.

Yep, switching is better. When you first choose, the odds of any box being the cash box are 1/3. When I show you one of the empty ones, I increase the possibility of the box I *didn't* show you to 1/2. Your box, chosen prior to my revelation, still only has a 1/3 chance. So switching is better.

It's called "The Monty Hall" problem, after the "Let's Make a Deal" game show host. Google for a better explanation. It took me over a week to get my head around this. Drawing out all the possibilities helps.

Dave

LittleToe

I think you'll find that when you do the math that statistically the odds improve to well over 50%

You're betting one card against two others, where one of which is already known.

There's a similar proposition using ten cards, that I was first shown. Its a real brain scrambler!

AlmostAtheist

You're right, Ross. The original choice has a 1/3 chance of winning, but a switched choice has a 2/3 chance -- double the original!

By switching, you are essentially getting to pick TWO boxes. By sticking with your original choice, you are only picking one.

The entire point is moot, of course, since Shelley's already knocked us both out and scrambled with the loot. But it was a fun exercise!

Dave

juni

Mathematically statiscally-wise this is true what you say..... makes sense.

But I've found when taking tests that one should always keep w/their first choice of an answer if they really don't know the answer.

How do you explain that Professor Dave??

Juni

Yet Another Math Problem

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