Yep! That's the crux of it (see cg196's explanation below). A quicker
way to work it out is as follows ...
If there is a 1/3 chance of the prize being behind the door you picked,
then there is a 2/3 chance that it is behind one of the other two doors
1 - 1/3 = 2/3
(total probability - probability it is behind the door you chose)
So we have a 2/3 chance that it behind one of the doors you didn't pick
One of those doors is opened, and there is no prize behind it. So the
probability of it being behind that door is 0/3 (zero).
So the probability of it being behind the other door that you did not
pick, is
2/3 - 0/3 = 2/3
(probability it is behind one of the doors you didn't choose minus
probability it is behind the door opened for you)
I do like Karl's gameshow analogy, though. Of course, Karl, you don't
know whether the prize is behind the door you have already picked, or
behind the other unopened door! Cheers, Matt
Matthew Dye
Department of Psychology
University of Southampton
Highfield
SOUTHAMPTON SO17 1BJ
U.K.
Tel. +44 (0)1703 594584 (Daytime)
Tel. +44 (0)1703 346906 (Evenings and Weekends)
Email: see header
WorkWeb: http://www.soton.ac.uk/~coglab/coglab/matt.html
FunWeb: http://www.soton.ac.uk/~mwgd/
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