A little Monday morning math.

My boyfriend and I were watching the movie 21, and in the beginning was a scene from a linear equations class, and they were discussing variable change. They used the example of being on a game show, and there being a car behind one door and a goat behind the other two. Player chooses door one. Host reveals that behind door three, there is a goat. Then offers to let the player switch doors. Student in the class explains that it’s more probable to get the car if you take the switch. Professor asks why. Student says that there was a 33.3% chance he picked the right door. When the goat was revealed, The percentage that the car was behind door two was now 66.6 percent so it’s better to take the switch. (I may not have explained this correctly, because I don’t understand the problem to begin with. I’m pretty sure I got it right though)

I tried asking my boyfriend, since he’s pretty good with math, but he couldn’t really find a way to explain to to me without “it just is…”

What I asked him, and I can’t figure out, are two things: 1) Why doesn’t the third door reveal just make it a 50/50 chance between the two doors? Why does the third door even matter anymore? 2) Why does the 33.3 percent get “dumped” on the door NOT chosen, instead of the door the player initially chose? In other words, why is it more probable to switch than to stay?

Note: I do not go to school. I do not have homework. I’m just really bad at math, and would like to understand this problem.