Cupcakes and Books and School and Math Brainteaser

At my school, our AWESOME librarian is giving every class who brought in all their overdue books by today homemade CUPCAKES. That includes my class. It is also her birthday tomorrow. Happy Birthday Ms.Y!!!

I am reading a great book right now, called "The Girl Who Could Fly". It's a bout, well, a girl who can fly, and gets sent to this school for kids like her, but it turns out the people who work there don't have good intentions for the kids and their special abilities. It'd really good- check it out!

I just finished my homework. It was doing the bibliography for my part of a group project on Madagascar. Gah, I keep spelling it M-a-d-a-g-scar.

As for the math part. I have a question thing for you.
You are on a game show. There are 3 doors. Behind 2 doors are goats, and the other door is a car. YOU WANT THE CAR (even if you don't, just pretend). You pick a door. Before it is opened, the show host opens one of the 2 remaining doors. It is a goat, because the host knows which door holds the car, and obviously wouldn't open that one. After the door has been opened, you have the choice to stay with your original door, or switch to the other closed door. If you switch, you have a 2 in 3 chance of getting the car. Weird, huh? Seems like it's 50 50.

So, why? Well, since 2 doors are goats, you have a 66% chance of originally picking a car. The only other goat door is opened, so therefore if you switch from a goat, you HAVE to get the car, since there is only 2 goats. True, you may have originally picked the car, but that is only a 33% chance (1 in 3), rather than a 66% chance. If this doesn't make sense, watch this video: http://www.youtube.com/watch?v=mhlc7peGlGg

We wrote letters yesterday to the mathematician you said that it was not 1/2 but 2/3. A lot of other mathematicians said it was 1/2, and she was a complete idiot. But we did a similar scenario in class about 420 times (30 per partner) and got about 2/3 winning and 1/3 losing when we switched.

What's awesome/fail/sad is that we humans are so stuck-up and refuse to admit we are wrong, even though there is plenty evidence to prove it.

WOW! Long post.