Nicola, it does matter. The mistake that we were making before was ignoring the fact that one door has already been discounted. When this happens, if you ‘start again’ then yes, the probabilities are 50:50. However, if you continue to take this opened door into consideration - the mathematically correct way of doing it - the maths turns out to be a conditional probability and the probabilities change to 33:67.

Have a look at the site Ben linked to, and you’ll see why in some detail.

Ben, Rich, etc - I don’t doubt that you’re right, and well done for all being a bit genius. But for the sake of argument I’m going to say that the problem refers to a “real-life” situation and I think in the majority of cases, a person in real life who was in that situation would say “righto - that third door’s out of the buggering way, it’s a 50/50 chance, I’ll just give it a random guess”. So the “conditional probability” can go on a nice journey up my rear end … oh I give up.

I may sound rather irate here. But trust me, I have serious issues with this problem. Ask Ben- I almost mauled him in Pizza Express when he tried to explain it to me again

None of them! Marilyn vos Savant is an American newspaper columnist who deals with mathematical and logical puzzles, as well as more traditional self-help advice.

She was the person who said that the probability would NOT be 50:50 and lots of mathematicians wrote in saying “You are wrong. Women can’t do maths” and after a long debate they finally conceded it to her. The story may have been axaggerated a little but that’s who she is at least.