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Topic: Monty Hall (umpteenth dup) (Read 1468 times) |
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Carnie_ville
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Monty Hall (umpteenth dup)
« on: Apr 24th, 2008, 6:15pm » |
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You are a contestant on the game show Let's Make a Deal, and emcee Monty Hall has a game for you to play. On stage are three huge doors, and he informs you that hidden behind one of the three doors is a brand new sports car, behind another is a donkey, and behind another is 400 pounds of bananas. (This may seem obvious, but your goal is to get the car, not the donkey or the bananas.) He asks you to choose one door, and you will win the prize behind that door. You choose, but before he reveals what you have won, Monty reveals what's behind one of the doors you did not pick, and it's not the car. Before revealing what lies behind the remaining two doors, he makes you one final offer: if you wish, you may switch from your choice to the other remaining door. The question is: Should you switch, should you not switch, or does it matter?
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| « Last Edit: Apr 24th, 2008, 11:55pm by towr » |
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Random Lack of Squiggily Lines
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Everything before 7/1/2008 is now irrelevant.
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Re: okay try this one temporary!
« Reply #1 on: Apr 24th, 2008, 6:20pm » |
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JUST SEARCH THE ANSWERS ALREADY
*ahem*
All the riddles you post, i must say, are in the wrong section, and you could search half of these answers by scrolling down.
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You can only believe i what you can prove, and since you have nothing proven to cmpare to, you can believe in nothing.
I have ~50 posts to hack a "R" into a "D". Which one?
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Carnie_ville
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Re: okay try this one temporary!
« Reply #2 on: Apr 24th, 2008, 6:22pm » |
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LoL well i did Under do it with most of my ones but i think my 3 ones are Hard
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temporary
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Re: okay try this one temporary!
« Reply #3 on: Apr 24th, 2008, 6:28pm » |
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switching has 2/3 chance of having the car.
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My goal is to find what my goal is, once I find what my goal is, my goal will be complete.
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ima1trkpny
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Re: Monty Hall (umpteenth dup)
« Reply #4 on: Apr 25th, 2008, 1:06am » |
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Switch. You double your chances of winning.
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"The pessimist sees difficulty in every opportunity. The optimist sees the opportunity in every difficulty." -Churchill
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gotit
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Re: Monty Hall (umpteenth dup)
« Reply #5 on: Apr 25th, 2008, 1:35am » |
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on Apr 25th, 2008, 1:06am, ima1trkpny wrote:| Switch. You double your chances of winning. |
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But how? The car will be behind one of the two doors. So the probability is 1/2. Thus, switch or no switch, it does not matter.
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ima1trkpny
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Re: Monty Hall (umpteenth dup)
« Reply #6 on: Apr 25th, 2008, 1:52am » |
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on Apr 25th, 2008, 1:35am, gotit wrote:
So the probability is 1/2. Thus, switch or no switch, it does not matter.
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Actually it makes considerable difference. I'll make it visual so you can see it better...
the mark over the whole thing will be the door you choose (X in this case). There are three possible scenarios so that's why I have 3 rows. "/" will be where the prize is and the blank bracket is the filler prize we don't want.
X
[ /] [ ] [ ] Scenario 1
[ ] [ /] [ ] Scenario 2
[ ] [ ] [/ ] Scenario 3
Ok, in S#1 because you have already picked the prize door, the MC has the option of showing you either one of the consolation prize doors so in this case switching would not win you the grand prize.
In S#2, you've chosen one of the two low prize rooms which means the grand prize is in one of the other two doors. The MC has to open and show you one of them and he can only do this with the consolation prize door which means the one he doesn't show you contains the grand prize.
S#3 is the same as #2.
So out of the 3 ways it can be done, by switching the door after the MC exposes a door, 2/3 times you win.
Whereas if you always stay with the same door, you'll only win 1/3 of the time. So your odds are doubled by switching the door.
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"The pessimist sees difficulty in every opportunity. The optimist sees the opportunity in every difficulty." -Churchill
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gotit
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Re: Monty Hall (umpteenth dup)
« Reply #7 on: Apr 25th, 2008, 2:09am » |
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Ummm...ok I get it now. You know, probability is one thing in mathematics that always confuses me ( and it's NOT the only thing in mathematics that confuses me  ).
Anyways, thanks for the nice explanation.
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Sir Col
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Re: Monty Hall (umpteenth dup)
« Reply #8 on: Apr 25th, 2008, 2:15am » |
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Yes, I was thinking the same, gotit.
Just when I thought, "Oh no, here we go again..." I came across your lovely explanation, ima1trkpny. Bravo!
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mathschallenge.net / projecteuler.net
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ima1trkpny
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Re: Monty Hall (umpteenth dup)
« Reply #9 on: Apr 25th, 2008, 2:16am » |
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No problem, anytime gotit. (Though you could have researched ) Don't worry about it, I had to see it drawn out too before I got the concept (visual learner).
on Apr 25th, 2008, 2:15am, Sir Col wrote:Yes, I was thinking the same, gotit.
Just when I thought, "Oh no, here we go again..." I came across your lovely explanation, ima1trkpny. Bravo! |
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Glad it made sense to you. I did a double take for a second when I came across this (missed it initially since I replied at the same time you did) Thanks.  You mean you hadn't heard of that before?
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| « Last Edit: Apr 26th, 2008, 6:20pm by ima1trkpny » |
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"The pessimist sees difficulty in every opportunity. The optimist sees the opportunity in every difficulty." -Churchill
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temporary
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Re: Monty Hall (umpteenth dup)
« Reply #10 on: Apr 25th, 2008, 4:35pm » |
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on Apr 25th, 2008, 1:35am, gotit wrote:
But how? The car will be behind one of the two doors. So the probability is 1/2. Thus, switch or no switch, it does not matter.
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If he knows what door has what, then there is 1 2/3 chance that you won't have it in the first guess, he reveals a dud, and switching gets the car. The other 1/3 is that you got it right to start with.
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iono
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Re: Monty Hall (umpteenth dup)
« Reply #11 on: Apr 25th, 2008, 7:46pm » |
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on Apr 25th, 2008, 2:09am, gotit wrote:Ummm...ok I get it now. You know, probability is one thing in mathematics that always confuses me ( and it's NOT the only thing in mathematics that confuses me ).
Anyways, thanks for the nice explanation. |
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you know, probability has a lot to do with solving this riddle http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_eas y;action=display;num=1208405307
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| « Last Edit: Apr 25th, 2008, 7:46pm by iono » |
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So, if I help you, I'll get kicked for ksing, but if I don't, then I'll get kick for not helping...
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jollytall
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Re: Monty Hall (umpteenth dup)
« Reply #12 on: Apr 26th, 2008, 1:55am » |
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Probably all the twists of this have been discussed many times. Still, I think this wording of the riddle is not 100% correct in the current version (very typical mistake in many well known riddles).
You must switch if we KNOW that an empty door will be opened regardless whether you chose the right one or not. This is to increase the tension and sell the show better.
If the instruction to the host from the producer (knowing the economic situation of the channel and the fact that you are smart) is that only show an empty window if you are right (otherwise immediately give you what you chose) then you should stick.
The opposite is also true. If the car should be given as part of the promotion contract with the car dealer, and so you get it immediately if you are right and offered to switch if not, then you should even more switch.
If the host randomly decides whether to open an empty door and offer the switch option then you should still switch (independent events).
Therefore the correct wording is that you don't say what is happening to you on the stage, but that you tell the rules of the game, i.e. an empty door is always shown. Then all 1/3 - 2/3 logic stands.
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| « Last Edit: Apr 26th, 2008, 1:57am by jollytall » |
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