[dba-Tech] Three Doors Problem

OK, here we go :-)

However, if you switch,  your chances increase to 1 in 2 (50%).

No they don't, they increease to 2 in 3 (67%)


(Don't feel bad if it doesn't sink in immediately. <g>)

-- 
Stuart

On 11 Sep 2012 at 9:20, Arthur Fuller wrote:

> Gustav,
> 
> Doesn't matter which door you pick initially. It remains correct in terms
> of probability always to choose to switch. No matter what your initial
> choice, you have a 1/3 chance of correctness. That leaves two doors. I open
> one of them to reveal a bad choice. At that point, if you stick with your
> original choice, your chances remain 1 in 3 (33%). However, if you switch,
> your chances increase to 1 in 2 (50%). I know it's difficult to see why,
> but if you prefer a little empirical evidence, try this:
> 
> Take 3 playing cards and 3 coins. I don't know Danish currency, so I'll say
> 2 pennies and 1 nickel, the latter being the "good" choice and the former
> the "bad" choices. Place the coins beneath the cards and then try out the
> alternatives.
> 
> Remember that I (or in this case you) know what's beneath each card, so
> that no matter which card you choose initially, the host is always able to
> turn a "bad" card.
> 
> Don't feel bad if it doesn't sink in immediately. When first published in
> Scientific American magazine, this caused a furor unlike anything in the
> magazine's history. Statisticians with strings of credentials as long as
> your arm fought against its answer, but eventually had to admit the
> correctness, no matter how counter-intuitive. Always switch.
> 
> Although not immediately relevant, I should add that for about three years
> I made my living playing backgammon, and played in dozens of tournaments
> including several world championships. I also played against some of the
> finest in the world at that time. I read every book published about the
> game and learned almost everything I know about probability from studying
> those books and the game itself. For centuries, it was almost entirely a
> game of luck. No one knows for sure, but sometime around 1920 the doubling
> cube was introduced into the game. That changed everything. The game became
> a study of probabilities, not a game of pure chance.
> 
> A.
> 
> On Tue, Sep 11, 2012 at 8:31 AM, Gustav Brock <gustav at cactus.dk> wrote:
> 
> > Hi Arthur
> >
> > That's a strange experience. I had to think about this, but when I
> > realised that initially you most likely had picked a bad door, then Stuart
> > is of course right - when a bad door is revealed, the door you didn't
> > select is most likely the good door.
> >
> > /gustav
> >
> >
> >
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