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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?
yes.
More exact phrasing:
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 [that is, booby prizes]. The car and the goats were placed randomly behind the doors before the show. The rules of the game show are as follows: After you have chosen a door, the door remains closed for the time being. The game show host, Monty Hall, who knows what is behind the doors, now has to open one of the two remaining doors, and the door he opens must have a goat behind it. If both remaining doors have goats behind them, he chooses one randomly. After Monty Hall opens a door with a goat, he will ask you to decide whether you want to stay with your first choice or to switch to the last remaining door. Imagine that you chose Door 1 and the host opens Door 3, which has a goat. He then asks you "Do you want to switch to Door Number 2?" Is it to your advantage to change your choice?
still yes.
Yes. You have a 1/2 chance of getting a car if you switch, but only a 1/3 if you stay put.
doesn't matter.
No.
It's now 50/50 whichever door you go for.
Wesley Snipes?
but it was 1 in 3 when you made you first choice.
You should always switch as you get a 66% chance of winning if you switch...
😀
Didn't I post a Monty Hall thread a couple of hours ago though?
[url= http://mathforum.org/dr.math/faq/faq.monty.hall.html ]Monty Hall Question[/url]
Surely this one has been done already?
You should switch as the probability is now 2/3 for the other door. End of.
Didn't I post a Monty Hall thread a couple of hours ago though?
I didn't see it. If I switch to that thread do I have a better chance at laughing at people?
miketually... nope.. I think I only got 2 replies, and one of those was from me!
Does it matter in what order you got the replies? 🙂
Yes, or at least 66% of the time it does... 😀
miketually - have you been reading The curious incident of the dog in the night time by any chance??
Switch every time, as waswas says. When you chose door 1 you had a 33% chance of being correct. Now you have a choice of 2, by switching you have a 50% chance of being correct.
Besides, if you end up with the goat you can't drive around but it's regular sex at least.
AAAAHhhh!!! Just open the frickin open the door!!! 😈
So, what about deal or no deal, when they get offered the swap at the end? there were 22 boxes, he's stuck with it all the way until there is just his box and one other. would it be better to swap?
Can I just take the goat behind 3? My lawn's a bit overgrown and I'm happy with my motor.
pk-ripper.. so close... you got the 33% bit, but once you take away the other door, the only door remaining must have a probability of 66%.
but I was right about the regular sex though.
tomzo - MemberSo, what about deal or no deal, when they get offered the swap at the end? there were 22 boxes, he's stuck with it all the way until there is just his box and one other. would it be better to swap?
It's a nice idea, but one that would only work if there were 21 boxes with (let's say) £1 in them and 1 box with £250,000. In which case if you were left with two boxes at the end and one was still the £250k box then you'd be an idiot not to switch as you'd have a 95% probability of winning the big prize by switching.