Monday 24 August 2009

Monty Hall, with the earthquake... and musings

...further to my last post...

So, when Monty opens the door, that does not alter the probability that the prize was in (b) - the two non-chosen doors. We know that regardless of whether the prize is in (a) or (b), he's not going to reveal the prize when he opens the door. When he opens the door what it does is guarantee that if it was in (b), it is now behind the one remaining (b) door, which now has the whole of the 2/3 probability to itself.

But, when the earthquake opens one of the (b) doors and shows the prize is not there, that does alter the (b) probability. The earthquake might have revealed the prize, but it didn't, so what it tells us is just that it's not behind that particular door. The prize is not behind that door but is equally likely to be behind either of the others. The (b) probability drops to 1/2 and the (a) probability increases to a half.

David Mackay has a much more rigorous explanation*. However, my point is that while I am now fully convinced that I 'understand' what's going on, my initial intuition has been twice overturned. For a while previously I was fully confident of the opposite opinion. So, how can I ever trust what I earnestly believe to be true? New insights might overturn what I believe. It's back to this idea of the provisional again. What we believe can only ever be provisional. That's the only knowledge on offer.

* If you want to read it, David Mackay has made his excellent book available for free download here. The problems are on page 57 and the solutions on page 61.

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