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can someone solve this math riddle for me - Page 5

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evanthebouncy!
Profile Blog Joined June 2006
United States12796 Posts
July 23 2007 12:47 GMT
#81
On July 23 2007 21:27 geometryb wrote:
Show nested quote +
On July 23 2007 12:45 evanthebouncy! wrote:
On July 23 2007 12:40 geometryb wrote:
if anyone needs more convincing, you can just write a program to run this 1,000 times.

in the first group, you make the person not switch.

in the second group, you make the person switch.

and keep track of how many times each person wins and see who wins more. this avoids all the thinking that makes my head hurt.


Or you can think this way:

You have 100000000000000000 boxes
You pick one, knowing you have 1/100000000000000000 chances
Host eliminate 999999999999998 boxes, 2 remains

You better switch.


if you want more experimental results then i guess.


Hun no lol It's merely there to help ppl visualize things better by exaggerating the situation, who's gonna experiment? We're talking theory here!
Life is run, it is dance, it is fast, passionate and BAM!, you dance and sing and booze while you can for now is the time and time is mine. Smile and laugh when still can for now is the time and soon you die!
evanthebouncy!
Profile Blog Joined June 2006
United States12796 Posts
July 23 2007 12:47 GMT
#82
On July 23 2007 17:44 JeeJee wrote:
i hated explaining monty hall problem to others, but i've foudn a really simple solution that everyone can clearly understand

you only lose by switching if you picked the right box to begin with. what are the odds of picking the right box to begin with?

that's usually enough =p


Genius
Life is run, it is dance, it is fast, passionate and BAM!, you dance and sing and booze while you can for now is the time and time is mine. Smile and laugh when still can for now is the time and soon you die!
geometryb
Profile Blog Joined November 2005
United States1249 Posts
July 23 2007 12:55 GMT
#83
On July 23 2007 21:47 evanthebouncy! wrote:
Show nested quote +
On July 23 2007 21:27 geometryb wrote:
On July 23 2007 12:45 evanthebouncy! wrote:
On July 23 2007 12:40 geometryb wrote:
if anyone needs more convincing, you can just write a program to run this 1,000 times.

in the first group, you make the person not switch.

in the second group, you make the person switch.

and keep track of how many times each person wins and see who wins more. this avoids all the thinking that makes my head hurt.


Or you can think this way:

You have 100000000000000000 boxes
You pick one, knowing you have 1/100000000000000000 chances
Host eliminate 999999999999998 boxes, 2 remains

You better switch.


if you want more experimental results then i guess.


Hun no lol It's merely there to help ppl visualize things better by exaggerating the situation, who's gonna experiment? We're talking theory here!


i was talking about my thing about writing a program to repeat the game thousands of times. :p

theory and people's thinking often leads to a lot of wrong answers because you never know if you missed something or made a mistake or were just wrong to begin with. it's like when I say, "theoritically, it should work" most of the time it doesn't.

so the best way to do it is. come up with a hypothesis based on your theory. and then test it with experiment. and if you're right, yippee. if you're wrong, oh no.
Frits
Profile Joined March 2003
11782 Posts
July 23 2007 20:37 GMT
#84
On July 23 2007 20:56 [r]h_probe wrote:
Show nested quote +
On July 23 2007 20:17 Frits wrote:
On July 23 2007 11:56 Chill wrote:
On July 23 2007 11:43 Frits wrote:
The monty hall problem is a very simple riddle.

Choice 1 will always stay 33,3% no matter what they do, and there's sure to be a price. So the odds of the remaining doors together are 100%. So if you have 2 choices, and 1 is 33,3%, the other one has 66,6% chance of being the price. (100-33,3)

The case in which it wouldn't matter which door you took is when they take away one of the choices without knowing if that was the prize or not. (In which case it would be 33-33.)

Everyone here should be able to understand that.


Counter example:
Monty Hall with 10 doors. You can switch or not switch. Don't switch = 10% chance to win. By your explination above, switch should = 90%.


Nope it still counts, what you forgot is when adding doors, obviously you have to divide the chance by that added amount.

Choice 1 will be 10% no matter what they do like I said right? And there's still sure to be a price so:

100 - 10 = 90 % chance of ONE of the 8 doors left being the right one.

90/8 = 11,25% of getting it right when switching.


Wrong!

Look at it this way:
10 doors
You choose one door ----> 1/10 chance of getting it right no matter what!
Out of the 9 other doors the host reveals 8


So essentially you are either choosing 1 of two groups:
The group of one or the group of 9 (of which 8 have been revealed)

Therefore it is a 90% prob of getting it right if you switch!
There is no "dividing the chance by that added mount"!

To further illustrate my point, lets make the problem even bigger: say you to choose a number between 1 in a million. There is 1 random correct number.

Then someone (who obviously knows what the number is) says it is either your number or it is a different one they tell you. You would have to be absolutely insane to stick with your number because it is a 1/1000000 shot no matter what where as the other number is 999999/1000000


What I did with more doors was asssume he still only reveals one, not all but one.

There's a 90% prob if he eliminates 8 doors yes, but you have to divide the chance by the amount of doors if there's more than one door left to pick besides the original.
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