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## #1 Re: This is Cool » The TV show Numb3rs and probability » 2005-11-23 16:31:11

Ya it is.... I finally get this yay. By one of the prisoners saying "name one of the other prisoner" or "eleiminate one of the other prisoners" is the same thing as saying "dont eliminate me" which is the same thing as saying in the first problem "I think its door blah".

## #2 Re: This is Cool » My 3D engine: reinventing the wheel » 2005-11-22 11:30:32

I so want to do this my self. Its really fascinating. It sounds like a cool holiday project for me.

## #3 Re: This is Cool » Poll: thousand million = billion? » 2005-11-22 11:20:31

Thats why I prefer the UK system.

However. I looks like my dreams of making the UK system the universal system is dimishing. The US system is becoming more and more universal. If theres one good point about the US system. It doesn't take a long time to say some of the bigger numbers which dont exacty fall on a nice "power of 6" or somthing.

## #4 Re: This is Cool » The TV show Numb3rs and probability » 2005-11-22 11:15:50

thanks, and thanks putting up with my ignorance...lol ahaha

## #5 Re: This is Cool » The TV show Numb3rs and probability » 2005-11-22 11:08:14

The idea was that the points didn't go to anyone

But now, I have changed the code

``````import java.util.Random;

class  NumbersThing
{
public static void main(String[] args)
{
Random r = new Random();
int worked = 0;
int didnt = 0;
for (int trys = 0; trys<100000000;trys++ ){
int guess = r.nextInt(3);
int takeaway=guess;
//Ensures the reveiled wrong answer is not
//the one you guessed
takeaway = r.nextInt(3);
}
int swap = -1;
for (int i = 0;i<3;i++){
if (i!=guess && i!=takeaway)
swap=i;
}
//System.out.println("Swap:     " + swap);
//It worked
worked++;
else
//Didn't Work
didnt++;
}

double ratio = (double)worked/didnt;
System.out.println("Swapping worked: " + worked + " times");
System.out.println("Swapping didn't work: " + didnt + " times");
System.out.println("Ratio: " + ratio);
}
}``````

Well the conclusion is, Ive been wrong. Im still confused though lol!

--output--

Swapping worked: 66668889 times
Swapping didn't work: 33331111 times
Ratio: 2.0002000233355557

-----------

So there you go.

Im deffinatly willing to accept my being wrong now!

The thing that I couldn't get my head around was, if you hadn't choosen one in first place. I couldn't work out what was the difference. Now I realise the difference is that you can choose one card that you dont want to be eliminated as being a goat. And by restricting the host to what he can remove thus it increses you chances on the swap.

This is a very good discussion. It has really opened my eyes...

## #6 Re: This is Cool » The TV show Numb3rs and probability » 2005-11-22 10:41:10

I know why 1/3 of the answers are missing, and its cause I was lazy. Rather than finding a door which wasn't the guess and which wasn't the answer, I simply picked a random number and if it wasn't the guess and wasn't the answer then I started from the top at the next itteration

shouldn't make a difference, but I try and go back and be more through if you like. I be back with modified code

## #7 Re: This is Cool » 0 = 1 » 2005-11-22 10:12:09

Yes, I am indeed. lol

Well done. heheh

I did know that my (deliberate) error is the (square root distribution rule) line.

## #8 Re: This is Cool » The TV show Numb3rs and probability » 2005-11-22 10:06:55

mikau wrote:

Something doesn't sound right there. You eliminated the selection. In your example, you said we will not make an official selection and reveal goat C every time. Am I correct?

C is just simply one that is not the car.

mikau wrote:

Pardon me if I'm not but If I am, what if you were to pick goat C when actually playing the game? The rules of the game state that when you pick one, one of the goats will be revealed, not the car, and not the one you picked.

Ok, lets just say that B "is" the car. Just to clarify
If I picked A then they would reviel C
If I picked C then they would reveil A

So you see it didn't matter whether I picked A or C in the first place. Im still in the same predicament. And obviously, if Id have picked B in the first place, then then I swap, I'd be wrong.

mikau wrote:

I read about computer simulations that proved this concept. Did you program it to make the selection, reveal a remaining goat that is NOT the one you picked, switch the choice, and check whats inside? Thats the only proper way to do it.

Thats exactly what I did. By all means,please, check it yourself.

``````import java.util.Random;

class  NumbersThing
{
public static void main(String[] args)
{
Random r = new Random();
int worked = 0;
int didnt = 0;
for (int trys = 0; trys<100000000;trys++ ){
int guess = r.nextInt(3);
int takeaway=guess;
//Ensures the reveiled wrong answer is not the one you guessed
while (takeaway==guess){
takeaway = r.nextInt(3);
}
//Makes sure the one reveiled was not the answer, if it was, the whole thing is discarded.
//Continue
int swap = -1;
for (int i = 0;i<3;i++){
if (i!=guess && i!=takeaway)
swap=i;
}
//It worked
worked++;
else
//Didn't Work
didnt++;

//JUST TO MAKE SURE!
if (swap == guess){
System.out.println("ERROR");
}
}
}
double ratio = (double)worked/didnt;
System.out.println("Swapping worked: " + worked + " times");
System.out.println("Swapping didn't work: " + didnt + " times");
System.out.println("Ratio: " + ratio);
}
}``````

-output-

Swapping worked: 33331990 times
Swapping didn't work: 33335219 times
Ratio: 0.999903135479626

-another output-

Swapping worked: 33330446 times
Swapping didn't work: 33338379 times
Ratio: 0.9997620460190941

## #9 This is Cool » Poll: thousand million = billion? » 2005-11-22 00:41:31

martian
Replies: 11

Although I cant seem to do actual polls on this forum, you can still post and give your thoughts.

???????????????????????????????????????????

Should "one billion" be equal to a "one thousand million" (1,000,000,000) or "one million million"(1,000,000,000,000)

???????????????????????????????????????????

I believe in the billion = "one million million" rule
and trillion = "one billion billion"
etc...

## #10 Re: This is Cool » 0 = 1 » 2005-11-22 00:08:35

0 = 1

and I can prove it and thus destroy mathematics for eternity ..... mauh hah ha ha ha ha

watch little kiddies as your perfect maths fails horribly

1 = -1 x -1              (I think we get that)
√1  = √(-1 x -1)      (square root both sides)
= √(-1) x √(-1)  (square root distribution rule)
= i x i                ("  http://www.google.com.au/search?q=square+root+of+-1  ")
1  = -1                  (√1 = 1)
1+1= -1 + 1
2 = 0
2/2 = 0/2
1 = 0

and there you have it!!! MATH IS DESTROYED MAUH HA HA HA H AH

## #11 Re: This is Cool » One divided by Infinity » 2005-11-21 23:34:07

eleusis is right

the lim(1/i) as i → ∞ = 0

what I really what to know is, what is 0/0 ???? heheheh that will stump a lot of you.
I can think of 4 possiblilities

1.
0 over anything is 0 thus 0/0 = 0

2.
anything over 0 = ∞ thus 0/0 = ∞

3.
anything over itself = 1 thus 0/0 = 1

4.
As a combination of the above 3 rules 0/0 = any and every number in exsistance including imaginary numbers

## #12 Re: This is Cool » The TV show Numb3rs and probability » 2005-11-21 22:51:13

100 000 000 times yes!!!

and I did that a few times, so really about 400 000 000 times

and yes "The past will never ever ever determine a greater probability for one posibility"
eg.
if you throw a dice 9 times, and a 6 comes up every single time (highly unlikely, but possible). What would be the probability of a 6 coming up on your tenth throw? ANSWER 1/6. Ive also run this simulation . Even though the chance that of throwing a 6, 10 times in a row is 1 in 60466176 if it has already been thrown 9 times, the next time is 1/6.

Its the same principle

So the probability started at 1-in-3 but then the host revealed one, the probability changes to 50:50.

## #13 Re: This is Cool » The TV show Numb3rs and probability » 2005-11-21 20:03:27

Sorry all you people who think this works. IT DOESN'T!!

Proof

The past will never ever ever determine a greater probability for one posibility. The fact that you made a decision before does not change the probability that you have 2 options, "swap" or "stay" and two posibilities "car" or "goat". The chance is 50/50 (FULLSTOP).

Imagine that you dont choose one to begin with!! Lets play this out. options A B C. They tell you to pick one (BUT YOU DONT). Knowing that they will not pick the "car" they show you that C is a goat. Then they tell you to "stay" or "swap". You dont have a orginal choice. SO WHATS THE PROBABILITY!!! You have to choose A or B. 1 is right, 1is wrong! The probability is 50:50. The same as if they never had a C in the first place.

If You still dont belive me then believe me when I say that Im a computer Scientist and I simulated the whole process in a computer and run the simulation ONE HUNDRED MILLION TIMES!!!!! The simulation showed that it swapping worked 50% of the times.

CONCLUSION:
NUMB3RS WAS WRONG!!