"Lets make a deal": door probabilities

One of the best Straight Dopes... interesting in a mathematical kind of way... but don't worry, totally understandable if you read it over and over.

Link

Suppose you're on a game show and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

"Exception that proves the rule"

This is from The Straight Dope, and it's one of my favourite sites.

http://www.straightdope.com/classics/a3_201.html

"I've looked up citations of this saying dating back to 1664, and in every case it was used in the brain-dead manner we're accustomed to today--that is, to suggest that non-conforming cases, by the mere fact of their existence, somehow confirm or support a generalization. Obviously they do nothing of the kind. We like to think proverbs become proverbial because they're true; this one is an exception. It certainly doesn't prove the rule."