If this is your first visit, be sure to
check out the FAQ by clicking the
link above. You may have to register
before you can post: click the register link above to proceed. To start viewing messages,
select the forum that you want to visit from the selection below.
You start out with a 1 in 3 chance and pick curtain #1. After curtain #3 is taken away there is still a 1 in three chance in all, but curtain 3 is gone so you have to pick between 1 and 2. You picked 1 at first and if it is 1 then your first pick at 1 in 3 odd was correct. Now that curtain 3 is gone if you change to curtain 2 you lose the game. All in all it was 1 in three and that doesn't change. Now that curtain 3 is gone if you switch to curtain 2 you have just taken a new chance based on what seems to be 50-50 odds but in fact it has always been 1 in 3.
If I started with 1 and it was actually 2 then changing to 2 would win the game but only because the car was behind #2 in the first place. If I had picked #2 in the beginning then switching to #1 would lose the game and staying with #2 would win it.
The fact of the matter is that the odds are set in stone because picking a different curtain doesn't change the location of the car. After #3 is gone you now have a 50-50 chance of picking the right one whether you stay with the one you have or switch.
Personally I would stick with my first pick because I would figure that the game show host is trying to influence my decision to something different by giving me a chance to pick something different.
If I knew that the game show had at its motive for the contestant to win more often than not then I might change my pick, figuring that the game show host wants me to win and that is the reason fot the second chance. But you know they're in it for the money and don't want to lose that car (although their commercial sponsors would certainly pay for it).
my math intuition tells me that the odds wouldn't change regardless of whether you switch or not. i've even studied advanced probability and stuff, because I as a math major in college and i have a great interest in the field. but i did some research into the monty hall problem, and the problem seems to be more complicated than i thought. so i don't know now.
people with PH'ds have sided with my initial argument, but apparently there's a lot of math involved in this. in fact, this seems like a very deep and intense math problem that I would avoid until I get a better understanding of probability.
Comment