Yer It does :) The essence of this problem is in the fact that the host isolates one of the goats. The combination of this and the fact that you don't know what your first guess was makes the permutative approach obsolete.
Wayne was absolutely correct in saying the approach is to think of it as 1 group of 1 and 1 group of 2... and thats pretty much the end of it. I have a couple of notes about the working below... > > This one always causes lots of discussion :) > > Work it out as a permutation problem. You have three doors, labelled 1, > 2 and 3. You have two goats (G) and one car (C). So the possible > unique permutations (since we don't care /which/ goat) are: Order is not important in this scenario, so there are actually only two permutations, because assuming you dont pick the goat, you will unveil both doors in that group if you choose that second group. C / GG 1/3 G / GC 2/3 if you want to expand it. C1 / G1G2 C1 / G2G1 G1 / G2C1 G1 / C1G2 G2 / C1G1 G2 / G1C1 You can see pretty clearly that the car sits in that first group only a third of the time. > > 123 > CGG > GCG > GGC > > So that tells us that for any one door, we have a 1/3 chance of there > being a car behind it and a 2/3 chance of getting one of the goats. > Let's choose a door and work some numbers: > > If we chose car (at 1/3 probability): > Host opens door 2 or 3 (50% each) Im not entirely sure what the 50% is of ? What relevance does it have to the puzzle ? Its not important which door is picked, as he chooses not randomly but the door with the goat. > Change - lose 1/3 > Stay - win 1/3 > If we chose either goat (at 2/3 probability): > Host opens door for other goat (always) > Change - win 2/3 > Stay - lose 2/3 Those two probabilities combined have over 1... Im not sure I follow your argument ? > > So, for each combination of 'change/stay' and 'win/lose' we have: > > Change: > win = 2/3 > lose = 1/3 > Stay: > win = 1/3 > lose = 2/3 They seem to fit, but Im unconvinced you have used the right line of reasoning...sorry to be a wet blanket :) Matt. _______________________________________________ Delphi mailing list [EMAIL PROTECTED] http://ns3.123.co.nz/mailman/listinfo/delphi
