[dba-Tech] Three Doors Problem

It's commonly known as the "Monty Hall" problem, after the compere of the TV show Let's 
Make A Deal.

It first appeared in American Statistician in the '70s.

I've discussed it at length on other forums.  It's amazing the number of very good 
programmers who just can't  follow the logic and won't accept the correct answer :-)

(BTW, the correct answer is - always switch - it gives you a 67% chance of picking the right 
door)

-- 
Stuart 

On 10 Sep 2012 at 22:29, Arthur Fuller wrote:

> This is old science, but perhaps it's time to trot it out again, if only
> because as I write this, I'm listening to a cbc-radio program called Ideas,
> whose current subject is probability. So allow me to trot out a problem
> that is a couple of decades old, and invite you to solve it without
> referring to Google or Scientific American (in which there occurred a very
> heated discussion that lasted about six months in Letters to the Editor,
> many of whose authors cited various credentials from prestigious
> universities). But in the end, math proved correct.
> 
> It's the classic three-doors problem, in the following descriptions of
> whose doors, feel free to substitute objects of interest, the only proviso
> being that two should be eminently desirable and the third an unpleasant
> alternative.
> 
> I am the host of a TV show. You are the contestant. You are presented with
> three doors.
> 
> Lights focus on me, and I announce that our new contestant is the
> lovely/handsome Mr./Ms. J.D. Something, a seasoned developer from
> Somewhere, Kansas and specializing in several programming languages.
> 
> Lights focus on you. In 30 seconds, you describe your current career,
> failed marriages, naughty children, and recent auto-accidents. Enough of
> the fluff! Time to move on to The Game.
> 
> Behind these three doors lie your three prizes, my darling/handsome
> contestant!
> 
> Behind two of these doors lies something ghastly, Behind the other is the
> answer to all your problems, and all your family's problems, forever!
> 
> I was going to get into ghastly descriptions of what lies behind the bad
> two doors, and a rhapsodic description of what lies behind the third, but
> let's strive for simplicity.
> 
> 1. Choose a door: A, B or C.
> 2. As host, I select one of the remaining two doors, revealing something
> ghastly.
> 3. I now invite you to switch your choice to the remaining door, or stick
> with your original choice.
> 
> Does it make a difference whether you stay or switch, and if so why?
> 
> Facts:
> This question originally arose in the pages of Scientific American about
> 40+ years ago, IIRC.
> It's only fair if you try to answer, and explain your answer, in about 20
> lines of text and/or algebra.
> I knew the answer even before the SA discussions began, and proved it using
> three playing cards, within 5 minutes.
> Many of the finest statisticians in the world argued about the answer for
> about six months in Letters to the Editor of said publication.
> 
> Provisos:
> Even though I have cited the source material and its ensuing lengthy
> discourse, if you want to play fair, please ignore the sources and deal
> with the problem at hand.
> 
> Miscellaneous:
> I got to the solution rather quickly, but only because I'm an expert at
> backgammon, which requires the ability to do a large number of calculations
> in a very limited amount of time. Thus I arrived at the correct answer
> rather quickly. This is not to say that expertise in backgammon is
> required, but that expertise in probability analysis helps.
> 
> Proofs are invited. (I haven't written down the solution in algebraic form
> lately, but given three cards, I can prove the answer within a couple of
> minutes.)
> 
> A.
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