A thoroughly honest game-show host has placed a car behind one of three doors. There is a goat behind each of the other doors. You have no prior knowledge that allows you to distinguish among the doors. "First you point toward a door," he says. "Then I'll open one of the other doors to reveal a goat. After I've shown you the goat, you make your final choice whether to stick with your initial choice of doors, or to switch to the remaining door. You win whatever is behind the door." You begin by pointing to door number 1. The host shows you that door number 3 has a goat.
Does your chances of getting the car increase by switching to Door 2?
Don't cheat.
5 comments:
Hmm...
I'll give you a little space in case you're still thinking about it.
OK. I pick a door. My chances of picking a car is 1 in 3. My chances of picking a goat are 2 in 3.
When the host shows me a goat, there's still a 1 in 3 chance I've selected the car and a 2 in 3 chance I've selected the other goat.
So since I had a better chance of selecting a goat originally, by switching I flip the odds, giving me the car 2 thirds of the time.
So yeah, switching to door 2 increases your odds of winning the car.
Oh and plz to more quiz of the day, it seems to have helped cure my hangover o' death. :)
Steve.
vhuyepq
Not all the time.
I've got a massive hangover this morning and work just doesn't sound like fun, so I'm kind of killing time until my brain wants to function properly.
And why am I a cheating fuck. :)
Steve.
ugreh
no
after he shows you the goat, you have a 1 in 2 chance of getting the car whether you change your mind or not
lbm
I decided to send out this little Quiz of the day around the office.
One of my fellow programmers was the only one to get the correct solution.
I am currently in the middle of two heated debates on the theory of the problem, even after supplying them with the Wiki article that explains the solution.
Steve.
mhkhm
failed... attempt 2...
ngwkotg
jesus fucking hell...
hbalceyy
That it is counter-intuitive is what makes it interesting.
FWIW, Steve is correct.. switching always improves your odds.
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