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HelicopterOff Topics › Bet all you math and logic wizzes won't get this one
06-02-2004 11:53 PM  13 years agoPost 21
spaceman spiff

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Tucson

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They way i look at is if the contestant choose the right door, the reason the host might play the game of eliminating a door is to entice him to pick the wrong door the second time around. So logically you are better off to stick with the first choice, unless of course the host thinks somebody might think he think the other person thinks that......then of course you have to consider that the host might think that the contestant thinks that he might think that the host thinks that..... in which case the contestant obviously chose the wrong door, unless of course the ....

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06-02-2004 11:59 PM  13 years agoPost 22
hingus2000

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wait i get it now: phil cole's explination is perfect.

Tom

T-Rex SA, Anodized Head, Gy240, 3s TP 2100mah, Align 35A ESC, 430L Motor

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06-03-2004 12:01 AM  13 years agoPost 23
ScareCrow_Delta

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Man, do we have lives other than RunRyder.com? Why did the chicken cross the road? I don't know? Why is SENECA ugly? I don't know?

~~~~ Defy the laws of gravity....gracefully ~~~~

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06-03-2004 12:28 AM  13 years agoPost 24
Torkroll

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ok someone make a little program that acts this out and uses a random generator and lets see the results of 1000 plays

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06-03-2004 12:36 AM  13 years agoPost 25
ScareCrow_Delta

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I did....50 50 chance becuase it was looping with 2 choices, not three, therefore 50/50. I looped it 2000, with random results everytime. I represented door1 as 1, door2 as 2. First loop result 1123 1's, 2nd loop results 823 1's. It is inconclusive.

~~~~ Defy the laws of gravity....gracefully ~~~~

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06-03-2004 12:56 AM  13 years agoPost 26
ScareCrow_Delta

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~~~~ Defy the laws of gravity....gracefully ~~~~

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06-03-2004 01:38 AM  13 years agoPost 27
helicopter34

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This is a famous problem. The chances are 1/3 and 2/3.

Think about it like this. I am going to use exxageration to drive my point home. Imagine if there were 777 doors at the start of the competition. You pick 1 door. What are the chances that you picked the car on your first try, 1/777, pretty low right. Then the game show host closes 775 of the remaining 176 doors. Now you are left with two doors, your original door and the only door the game show host didn't close. Come on guys!!! think!!!
remember: when you originally picked, there was a 176/177 chance that you didn't pick the correct door and that the car was behind one of the other 776 doors. If you switch to the only other door that is still closed after the host shut 175 doors, then you have a 176/177 chance that the car is yours.

Remember, the assumption behind using probability in the way were (you divide the number of right outcomes by the number of total outcomes and using that as your probability) is that there is no bias in the selection of the outcomes. However there is a bias in the selection of the two doors to be used in the final choice, one was selected from a pile that was more probable to have a car in it.

"A man flips a coin 3 times and it comes up heads.
What are the odds that it will come up heads again on the next flip?
50% of course. The previous flips have nothing to do with those odds.
After the empty door is exposed, the odds go from 1/3 to 1/2 but there is no justification to change choice. The odds are still 1/2 once the choice is between two."

yes you are correct about the coin because each successive flip has nothing to do with the previous flip, but with our situation with the doors, there wasn't an unbiased selection of possibilities.
Heres an example: if you have two bags of 1000 marbles, 1 bag has 999 blue and 1 red, and the other bag has 999 red and 1 blue. If I pull one marble from each bag without you seeing put one marble in my left hand and one in my right hand and say "pick a hand" and I tell you if you pick a hand with a red marble you win a car. Well there are two hands and each hand can have two possibilities: red or blue so "it doesn't matter, theres a 50:50 chance right?" Wrong, there is an unnaccounted for bias in the possibilities that supercedes simple probability.


"Hmmm, not sure I agree with this statement. I can say that the probability of a fatal plane crash is 1 per 1,000,000 hours, whilst a fatal car crash is 1 in 10,000 hours. Just cos they don't have equal probabilities of catastrophe doesn't mean I can't use a probabalistic approach to determine which mode of transport to use...."
I'm kinda talking about something a little different, I haven't really ever taken any courses in stats or prob, just doing some ramblings. Your write, you can obtain probabilities from statistics (divide the number of deaths by the number of car rides per year and you get the probability of dieing in a car ride), but what Im kinda talking about isn't probability I guess. What I am talking about is more along the lines of saying: if you have a specific car traveling on a road and you freeze it in time and analyse what you think will happen int he next instant, whether that particular car will crash, depends on the wind, whats in front of the car, the stresses in the metals, in fact every single force on every single atoms in the car and the surroundings (far greater variables to account for than is possible, but in theory the variables exist to be counted), then the car will either crash or not crash.

"This is where chaos theory comes in right? Infinitesimally small changes in initial conditions can have drastic effects on the output, therefore it is impossible to predict the outcome of a complex system accurately. Also Heisenberg's Uncertainty Principle says you can't measure anything accurately cos you'll change it in the process."
Sorta, I am not claiming to be an expert on any of this, but from what I know about caos theory: thats not really what I was talking about, I wasn't talking about the possibility of a person actually measuring and calculating these things.

What coas thoery has to say about our situation: there are governing equation (ones almost infinitely complicated that noone could utilize them) dictating everything that goes on (to some unquantum mechanical sense). In general these equations are extremely high order equations. Well if the system isn't that quaotic, the higher order terms are relatively small and you can sorta predict outcomes by approximating the system with low degree equations, but if the system is choatic then the higher order terms come in to play (and we don't know the higher order terms because the equations would be too complicated) and small changes become amplified so that approximations are meaningless.

The thing with Hiesenberg, it gets complicated with q-mechanics and introduces an almost randomness to systems on the quantum level that you couldn't even theoretically predict stuff. But what I was saying with respect to determinism is that even with randomness you can show how human free will can not exist.

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06-03-2004 01:44 AM  13 years agoPost 28
helicopter34

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Crap

No more time "philosophizing" I need to fix some helis.

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06-03-2004 01:53 AM  13 years agoPost 29
rotormouth

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Irvine, California

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wins: 3,335,164
losses: 1,664,836
iterations: 5,000,000

Yup, you certainly increase your odds if you switch after one door is opened, as proven in the above stats (assuming my code was good).

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06-03-2004 04:40 AM  13 years agoPost 30
John W

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Chelmsford, MA

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Your "percentage" of chances of winning from choosing 1 of:

3 Doors = 33 1/3%
2 Doors = 50%
1 Door = 100%

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06-03-2004 08:26 AM  13 years agoPost 31
nheather

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Horsham, West Sussex, UK

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helicopter34

If you really believe this why don't to try it. Get a friend to play the part of the quiz show host and get three playing cards (say a queen and 2 aces). Obviously you have got to find the queen.

Get the 'host' to lay out the cards so that he knows where the queen is. Pick one. Ask him to uncover one of the remaining cards (an ace of course). Change your choice and see if you have the queen.

Repeat this say 50 to 100 times and record how many times you win. The consensus is split beteen 50% and 66.666%. Even in a small sample of 50 you should be able to see which is correct.

I'm going for 50%.

Cheers,

Nigel

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06-03-2004 09:03 AM  13 years agoPost 32
helicopter34

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New Jersey, exit 82

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Interesting

http://www.cut-the-knot.org/hall.shtml

it is also an illegal form of gambling. You can definitely make a lot of money playing this game with your friends.

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06-03-2004 09:19 AM  13 years agoPost 33
jerrythercpilot

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Spaceman spiff,
I agree with you.

Now heres one to really separate the men from the boys:


Your in your car traveling at the speed of light and you turn your headlights on...what happens?

Light travels faster than sound, thats why some people appear so bright UNTIL you hear them speak.

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06-03-2004 09:36 AM  13 years agoPost 34
nheather

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helicopter34

Thanks for the link. I did the test and it came up more or less 2/3 but I was still doubting.

So I went on to read the text in Solution #1, this is the best explaination I have seen and it got me to draw out some logic trees myself. As a result I now fully understand it and am converted to the the 2/3 probability.

Hard to explain, but basically

Your first choice has 2/3 chance of being wrong - everyone agrees with that I think.

If you are wrong (and that is the most likely) and you swap then you are 100% likely to win.

2/3 * 100% = 2/3 = chance of winning with swap

If you are right (and that is least likely) and you swap then you are 100% likely to lose.

1/3 * 100% = 1/3 = chance of losing with swap

Cheers,

Nigel

p.s. Still have this niggling feeling that I've been scammed though

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06-03-2004 09:54 AM  13 years agoPost 35
helicopter34

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New Jersey, exit 82

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speed

"Your in your car traveling at the speed of light and you turn your headlights on...what happens?"

Firstly, nothing with mass can travel the speed of light. But even at 99.999999% the speed of light, if you were to shine a light, you would see the light travel ahead of you at the speed of light.

Thats the basis for the theory of relativity. Einstein and Lorenz fit their equations to the premise

1.) Light always travels the speed of light from every reference frame
2.) Newtons laws are the same in every reference frame

Its not that hard to accept because when traveling at 99.999999% the speed of light, you still sense yourself as standing still from your reference frame.

Its weird because to you, you see the light waves traveling away from you at the speed of light, but from someone who sees you traveling at 99.999999% with respect to their from sees that the light is only "beating you" by 0.0000001% the speed of light or 30 meters/second. If you could only catch that light, then you would have something....

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06-03-2004 09:59 AM  13 years agoPost 36
jerrythercpilot

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Hey wait a minute...I think your all wrong.

The probability of making the correct choice initially is 33.3%. Now the host forces you to make another choice (additional probability), do you stay with what you chose already (1/3 probability) or choose the other remaining door (an additional 1/2 probability). Now then, the total probability that you will choose the right door is 33.5% * 50% or if you prefer (1/3)*(1/2) = 1/6.

Think about this. If the hosts' job is to make you loose, he just reduced your total odds to 1/6 and you didn't even realize it.

Light travels faster than sound, thats why some people appear so bright UNTIL you hear them speak.

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06-03-2004 10:03 AM  13 years agoPost 37
Davo

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London, UK

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(1/3 probability) or choose the other remaining door (an additional 1/2 probability)
Hmmm, your probability options only add up to 5/6. That isn't possible, what's the other option for the remaining 1/6?

I think this problem is most easily explained with a tree diagram as nheather pointed out. You start off with three branches of probability one third, you make your choice and then the other two branches are truncated into one option. This truncated option MUST have a probability of 2/3 of being correct. So take it.

The problem gets clouded when issues such as game show host tactics come into play.

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HelicopterOff Topics › Bet all you math and logic wizzes won't get this one
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