When you pick yours the first time, you've got a 1/3 chance of being right. Him telling you that one of the other two isn't the car gives you no new information about the one you picked to begin with -- you already knew that at least one of those other two wasn't a car. You've still got a 1/3 chance of being right with the one you picked. But that leaves a 2/3 chance of being wrong, and that 2/3 chance is now entirely on the still hidden unpicked one.
(I really can't figure out a good way to explain this entirely. The way I was able to totally convince myself was just to set up all the different possible situations and look at the results.)
If you can't explain it to me, Hil, I don't feel so bad about not getting it.
Let's say that the car is in door 1. If you picked door 1, then you'll get it if you stay. If you picked door 2 or door 3, then you'll get the car if you switch. There's a 1/3 chance you picked right on that first try, but a 2/3 chance you picked wrong, so in 1/3 of the cases you'll get the car if you stay, but in 2/3 you'll get it if you switch.
I'm glad others are confused because I din't get it last night.
What's at the core of the problem? Being given the chance to switch to a card that has a 1/2 chance of being the right one? I mean, 1/2 if you started from step 2?
You know, this might be one I just accept, or run the numbers on. My big issue is that I want there to be some calculation that gets you from the odds on the first pass to the new odds, and I just can't see it.
What's at the core of the problem? Being given the chance to switch to a card that has a 1/2 chance of being the right one? I mean, 1/2 if you started from step 2?
I think the core of the problem is that the odds don't change. You've got a 1/3 chance of being right, 2/3 chance of being wrong. Suppose they don't tell you "door 2 is not a car." They just say, "You can stay where you are, or you can switch to doors 2 and 3. If either of those is a car, you get it; if neither of them is, you don't." That's an equivalent problem -- knowing which door of 2 and 3 is the one without a car doesn't change anything.
Aha! All the potential lives in the one card. I'd still rather see some multiplication, but I can live with that.
Think of it from Charlie's point of view. You pick one card from three. That leaves Charlie with three possible combinations of two cards:
goat/goat
car/goat
goat/car
Charlie reveals a goat card. The three possibilities for his hidden card are reduced to:
goat
car
car
If you switch with Charlie you go from one chance in three to win, to two chances in three.
I also need to start working on the Miracleborns. What, 6 hours in the car with a baby could be fun!
Specially now that we have the Miracleborn Stealth MiniVan.
Tim, the manager of Emmett's Little League Team, is gone this weekend so I'm running the team.
The last time I was in charge of running the team Emmett broke his nose.
Wish me some safe-ma today.
On the plus side, I get to set the pitching and positions for today and tomorrow's game. Fantasy Manager Land!
JZ continues her community service (for parking tix) by spending all day at a Circus Arts Benefits performance. It's a long day, but on the whole considerably more fun than picking up trash along the freeway.
And tomorrow is our paper anniversary.
