Monty Hall answer and final clarification

And the answer is..... switch doors. When you chose your door you had a 30 percent probability of choosing the car. After the other door is open and reveals a goat in essence your chosen door has stayed at 30 percent however the other door has picked up the probability from the opened door. As for the random vs. Monty Hall playing the game and knowing what was behind the door, for a single trial it doesn't matter so long as the door that is opened reveals a goat. On multiple trials it is a little different, since you would expect that the door with the car would be revealed a third of the time if it was truly random. The following link explains the problem a little better and also has an applet that will let you run the problem on a single trial, 10 trials, 100 trials and 1000 trials.
www.statisticalmisconceptions.com/MiscAndInvite05c.html
I was playing with it the other day and ran a dozen single trials and got a fifty fifty turn out. The problem really reveals itself over multiple trials (like 50 or more). It also runs on the assumption that the door opened never reveals the true prize. Which brings up another dilemma. Humans are horrible at creating randomness. We just can't do it. So in research, we use computers to generate random numbers. The problem is how can you program a computer to create random numbers, when the computer runs off of a mathematical algorithm that given enough data you could solve for, so is it truly random?

Monty Hall continued...

I will defer to Serge's comment that the host always opens a door with the goat. That was the original version I encountered. The most recent version I encountered Monty randomly opened a door revealing a goat. In terms of the problem (and I may be wrong) it doesn't matter whether Monty knows or not so long as it's a goat. Serge can correct me on that if I am way off, I guess I need to assess whether we are dealing with family wise or individual case error. (For those in the know I am intentionally using vague phrasing to avoid giving away to much).
-Josh

It's Been a while and Monty Hall

So the craziness that is finals just got over. Thus the delay in posts. Carol probably would have posted, but I have been monopolizing the computer. For some reason my professors want me to turn in work (I feel like I have been writing for weeks), and my students want grades. Go fig. Anyway, I am now officially finished with this semester. Three weeks off and then back to it. I am taking two classes over the summer, working on research, and teaching Stats again. And speaking of stats, I just recently restumbled upon this little gem. It is known as the Monty Hall problem. Now, I specifically know that some have already heard this and will no the answer already. For those of you who haven't heard it here is how it goes.
You or your friend (doesn't really matter just a different version) are playing a game show in some third world country, that really likes goats and cars. The host's name is Monty Hall. You are in the final round and the host reveals three doors. Behind one of those doors is a new car. Behind the other two are goats (actually this is really similar to the game show Deal or No Deal). You pick a door. We will say door A. Monty Hall then randomly opens one of the unpicked doors, we will say door C, revealing a goat. Monty Hall then turns to you and asks, "Would you like to switch doors to door B?" So that is the Monty Hall problem, do you switch doors from A to B or stay with A? I will give the answer in a day or two. In the mean time I look forward to hearing your guesses, and tell me why.
-Josh