Math Is Fun Forum

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.

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 answer = r.nextInt(3);
			int guess = r.nextInt(3);
			int takeaway=guess;
			//Ensures the reveiled wrong answer is not 
			//the one you guessed 
			//or the right answer
			while (takeaway==guess || takeaway==answer){
				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);
			if (swap==answer)
				//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...

Yes, I am indeed. lol

Well done. heheh

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

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

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!!