Taking into account the fact that the presenter opened a different door
there are two different scenarios.

1. The presenter opened a different door because you chose correctly and he's trying to throw you off, in which case there is a 100% probability that your original choice was correct.

2. The presenter didn't care which door you chose originally and is just trying to screw with your head and/or pad out the show, in which case there is a 50% probability that your original choice was correct.

Combining the two (and this is where my memory of probability math fails me - but it was nearly 30 years ago), there is then a 75% chance that your original choice was correct, so you should stick by it.
( argyleblanket The man on the roof works for me, Sun 16 Oct 2011, 9:36, 1 reply)

But since the host always opens a door
...what his motivation is doesn't matter. And I'd argue with that 50% figure as well - see my reasoning above :)

(This is an example of the Monty Hall problem, by the way.)
( Legionary - My god, Brian, there's a message in my alphabets, Sun 16 Oct 2011, 12:18, closed)