VERY INTERESTING!

From what I see everyone is right - it is both 2/3 and 1/2. It depends from when you are measuring the probability of an event.

I seem to remember from my university days that in probability we have the phrase 'given that....' and that there is a difference between measuring the probability of an event from end to end (i.e. from the whole of the group of events) and the final or single event (e.g after all but one of the events have occured). Therefore, we need to decide whether we are measuring the probability from the BEGINNING of the whole chain of events or whether we measure the probability of the final event.
So, we have: 'given that someone has chosen a door and the host has shown a goat etc etc' and we are then left with two coices - one is a goat and one is the prize. AT THAT POINT there is a 50/50 chance - whatever has gone before is irrelevent. However, at the begininng of the whole chain of events - i.e. before we have made our first choice - there is a 2/3 choice of winning if we swap as per the example. Both are right....... but it depends whether you measure from the the beginning of the whole game or just the final choice..

Any comments?