Unfortunately it's not a case of whether you agree or not
it's whether you can prove without doubt that your
interpretation is correct. The problem at hand is not new
and has been around confusing individuals like you and me
and people with much higher statistics knowledge for a long
time. That's why I sat down and wrote some pseudo-code and
when I saw the result I didn't initially beleive it so I
converted it to Delphi code and ran it and what do you know
the 33%/66% logic is correct.
People are failing (including me initially) to see that the
initial choice has 33% chance of success whether the host
tells you about the goat or not because you simply don't
have that knowledge when you made that choice. Essentially
the contest is giving you the chance to go with 1 door (your
initial choice) or 2 doors. i.e. a one third/ two third
split.
Here's another way to look at it: If the host had said to
you go ahead and pick a door but I'm telling you now if you
pick one of these two doors I'll give you a hand by showing
you one has a goat behind it. Whilst you don't know which of
the 2 doors he's refering to yet you'd be fairly silly to
not pick the 2 door option.
----- Original Message Follows -----
> You guys have too much time to waste :-)
>
> I can't agree. Surely the situation is just the same as
> if you started with 2 doors and had to choose between the
> two. I'm fairly sure if this scenario was performed a
> hundred times, and everyone was instructed to change their
> mind and choose the other door, roughly 50 people would
> win the car.
>
> Ross.
>
> ----- Original Message -----
> Look at the problem from an algorithmic point of view.
> Below is some simple Delphi code to test the logic. Read
> the code before you try to run it. If your logic
> evaluation is any good you should be able to see why you
> have 66% chance if you change versus only a 33% chance if
> you stay with your original choice. The key is the if
> statement and the fact that whilst the host has helped you
> out after you first choice by picking a wrong door for you
> the door with the car behind it hasn't changed and your
> original choice is therefore still only successful 33% or
> the time.
>
> procedure TestLogic;
> const
> LOOPS = 1000;
> var
> DoorWithCar: Byte;
> i: Integer;
> DoorChoice: Byte;
> FirstChoiceCorrect: Integer;
> ChangedChoiceCorrect: Integer;
> begin
> Randomize;
> FirstChoiceCorrect := 0;
> ChangedChoiceCorrect := 0;
> for i := 1 to LOOPS do
> begin
> DoorWithCar := Random(3) + 1;
> DoorChoice := Random(3) + 1;
> if DoorChoice = DoorWithCar then
> Inc(FirstChoiceCorrect)
> else
> Inc(ChangedChoiceCorrect);
> end;
> ShowMessageFmt('Original choice = %.0f%%'#13#10'Changed
> choice = %.0f%%',
> [FirstChoiceCorrect / LOOPS * 100,
> ChangedChoiceCorrect / LOOPS * 100]);
> end;
>
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