Weekly Riddle #2
Ferraris and Goats
Friday, February 18, 2005 by thethimble | Discussion: WinCustomize Talk
This riddle/annoying problem, as I'm sure most of you have seen/heard before, is definitely one of my favorite. So, here it is:
Imagine you were taking part in a game show. You've won through to the last round, which is a game of chance. There are three doors - all you have to do is to choose which door you want to open - Door 1, Door 2 or Door 3. Behind one door is a Ferrari. Behind each of the other two is a goat. Let's assume that you are normal enough to want a Ferrari.
After a moment's indecision you plump for a door - let's say it's Door 2. The gameshow host nods, knowingly. "Okay," he says, "I'm going to give you a final chance to change your mind. And I'm even going to help you." He opens Door 3 and shows you there's a goat behind it. "Now," says the host, "do you want to stick with the door you chose, or do you want to change to another door."
The question I ask you is subtly different. Should you stick with the door you chose, should you change (presumably to Door 1), or doesn't it matter in probability terms whether you stick or change?
Those of you who know the answer, please don't cheat. I HATE cheaters. Those of you who have never heard of this problem, guess as you wish. I will post the correct answer and solution as soon as someone guesses wrong. Happy Thinking
Imagine you were taking part in a game show. You've won through to the last round, which is a game of chance. There are three doors - all you have to do is to choose which door you want to open - Door 1, Door 2 or Door 3. Behind one door is a Ferrari. Behind each of the other two is a goat. Let's assume that you are normal enough to want a Ferrari.
After a moment's indecision you plump for a door - let's say it's Door 2. The gameshow host nods, knowingly. "Okay," he says, "I'm going to give you a final chance to change your mind. And I'm even going to help you." He opens Door 3 and shows you there's a goat behind it. "Now," says the host, "do you want to stick with the door you chose, or do you want to change to another door."
The question I ask you is subtly different. Should you stick with the door you chose, should you change (presumably to Door 1), or doesn't it matter in probability terms whether you stick or change?
Those of you who know the answer, please don't cheat. I HATE cheaters. Those of you who have never heard of this problem, guess as you wish. I will post the correct answer and solution as soon as someone guesses wrong. Happy Thinking
thethimble
Reply #2 Friday, February 18, 2005 6:48 PM
Reply #2 Friday, February 18, 2005 6:48 PM
Good job SD, any reason why? Or even better, what is the probability of winning a ferrari?
Suriken
Reply #4 Friday, February 18, 2005 7:21 PM
Reply #4 Friday, February 18, 2005 7:21 PM
... "Behind one door is a Ferrari."
i think that answers it, does it not?
(no I have never heard the riddle before either)
i think that answers it, does it not?
(no I have never heard the riddle before either)
thethimble
Reply #5 Friday, February 18, 2005 8:51 PM
Reply #5 Friday, February 18, 2005 8:51 PM
Ok, you guys are all wrong... Go back to the start. What was the chance you had the right door? 1 in 3. In two cases out of three you would have picked a goat. That holds true whatever. Then the host helps you out by showing you that one of the other doors definitely has a goat behind it. So, in fact you should always change your choice to the other door that wasn't opened. That way there's a two in three chance that you win.
If you think about it enough, you might actually increase your iq past 40!
If you think about it enough, you might actually increase your iq past 40!
thethimble
Reply #7 Friday, February 18, 2005 9:29 PM
Reply #7 Friday, February 18, 2005 9:29 PM
| I would geuess door one. Don't want that goat too close to a Feerrari. Only a guess |
Lantec
Reply #9 Friday, February 18, 2005 9:34 PM
Reply #9 Friday, February 18, 2005 9:34 PM
Actually you proposed that we had chosen door 2 and after elimninating door 3 the answer to your "question" is that there is no reasont o change your choice because there is no statistical advantage to changin it. And I disagree, odds change as events change. By opening door three you have now made the odds of selecting the right door 1 in 2. SAme as in playing cards. The more kings lying face up on the table the less chance you will draw a king from the deck. Nice try anyway.
mrtee
Reply #10 Friday, February 18, 2005 11:28 PM
Reply #10 Friday, February 18, 2005 11:28 PM
It's from Lockergnome, about helping seniors with problem solving (Sherman's Senior Helpers). It's called the Monty Hall effect.
CHANGE door choice. The odds are better.
CHANGE door choice. The odds are better.
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Reply #1 Friday, February 18, 2005 6:22 PM