Brain Teasers, Riddles, etc...

[Albatross]

*giggle*

Wow. We have Helios and Disch and Chris and Blackcoder and Grey Wolf... all arguing about something so simple...

Nice probability tree, BTW, Chris. So I have a 50/50 chance of shutting or upping? Is that it? EDIT: My tone is playful, for your reference, Chris.

Zykker is the only one who got the right answer to the problem I wrote. As far as the answer to the generic probability problem, I'll just sit back and watch you lot duke it out. I wonder how this will come out.

Actually, I should draw my own probability tree...

-Albatross

[chrisname]

@Albatross,
I would have thought the smiley-face made it obvious that I was joking... Your tone makes me think I would have been wrong.

[Seraphimsan]

ITT: math and science majors/hobbyists arguing over the probability of getting a non existent donkey at a hypothetical game show. Fun times. :P


EDIT: Also chris, please show me your magic ways of hearing tone in text T_T i've been trying for years :P

[chrisname]

Seraphimsan wrote:

ITT: math and science majors/hobbyists arguing over the probability of getting a non existent donkey at a hypothetical game show.

The truth. Then again, donkeys do exist...

please show me your magic ways of hearing tone in text

Tone doesn't mean sound in literature (and a post on the Internet counts as literature here): http://en.wikipedia.org/wiki/Tone_%28literature%29

[Albatross]

*rolls on floor laughing*

Posts on internet? In a C++ forum of insane geeks?! Literature?!? WHOO!

*Albatross was unable to sign the post because said albatross was laughing too hard*

EDIT: Gender-related typo.

[Disch]

Man I so want to post, but it will have to wait unil after work =(. I check out those links Grey Wolf posted then.

I'm positive it's 50/50. Either that or I'm misunderstanding the question (doubtful).

I guess this is just one more reason I hate Monty Python.

[Albatross]

What does Monty Python have to to with Monty Hall?!?

-Albatross

[chrisname]

(I think it was a joke)

[firedraco]

It is 2/3. I also was confused at first but the grouping pictures in the wiki article helped me understand it.

[tortillahead]

Guys, chill about the Monty Hall thing.

It is a 50/50 chance if you switch, look: http://en.wikipedia.org/wiki/Monty_Hall_problem

[Disch]

whoops, I misread Monty Hall as Monty Python.

Haw

[z05DSL3A]

tortillahead, go read it again.

[Duthomhas]

It is a common statistical problem. I was dimwitted to have missed it. While it flies in the face of normal people's common logic, the reality is that previous choices do affect later choices.

Grey Wolf has since posted enough links to the Monty Hall problem. Time to go read some.

[tortillahead]

@Grey Wolf
2/3's, my bad

[z05DSL3A]

Simple simulation:

#include<iostream>
#include<cstdlib>
using namespace std;

int doors[ 3] = { 0, 0, 0};
int choice;

void clear_doors( void);
void draw( void);

int main()
{
	long int n, wins = 0, wins_swapping = 0;
	double percent, percent_swapping, n_copy;
	
	cout << "Give number of games: ";
	cin >> n;
	n_copy = n;
	
	srandom( time( NULL));
	
	for( n; n > 0; n--) // this loop is for games without switching
	{
		draw();
		
		if( doors[choice] == 1)
		{
			// If the contestant stays with the chosen 
			wins++;
			clear_doors();
		}
		else 
		{
			// if the contestant swaps
			wins_swapping++;
			clear_doors();
		}
	}
	
	cout << endl;
	percent = (wins / n_copy)*100;
	percent_swapping = (wins_swapping / n_copy)*100;
	cout << "Number of winning games without switching: " << wins << " [ " << percent << "% ]" << endl;
	cout << "Number of winning games with switching: " << wins_swapping << " [ " << percent_swapping << "% ]" << endl;
	
	cout << endl;
	return 0;
}

void clear_doors( void)
{
	doors[ 0] = doors[ 1] = doors[ 2] = 0;
}

void draw( void)
{
	doors[ random() % 3] = 1; // places the car
	choice = random() % 3;    // picks one door at random
}

Give number of games: 1000

Number of winning games without switching: 355 [ 35.5% ]
Number of winning games with switching: 645 [ 64.5% ]

[Disch]

Ack!

Yeah I see it now.

Damn! Now I feel the fool. I let my arrogance get the best of me. I really was convinced I was right, but I guess I wasn't.

At least this made me feel better:

wikipedia wrote:

no other statistical puzzle comes so close to fooling all the people all the time" and "that even Nobel physicists systematically give the wrong answer, and that they insist on it, and they are ready to berate in print those who propose the right answer."

So I guess that means I have the mind of a Nobel physicist!

[blackcoder41]

What do you think is the ratio of male : female in this forum?

[edit]
Could anyone write a simulation? The problem is that there is no given data. Maybe someone have to base it on how much female are interested in programming.

[Zykker]

So like... Did no one pay attention to my post on how the only reason the host would ask you is if you had the right door to begin with? Actually it was Albatross's post, but still. If you were told by someone who is in on the trick tells you that you will have a chance to switch then is it not more logical that he would only ask if you were right. You could make a big deal out of it and get the switch but why would you if you had no reason to want to switch? Its a trick-trick question. Very Clever.

[helios]

the only reason the host would ask you is if you had the right door to begin with?

That's retarded and wouldn't work on a real game show. Regular viewers could catch on.
Also, the question is specific:

when you choose [a door], Monty will open one of the other doors, revealing a donkey, and give you a chance to switch your door.

At no point is it even hinted that the host gives you another chance only some times. Rather, it clearly states that a player will be given a chance to switch no matter what.
And, as has been demonstrated in the thread, offering a player a chance to switch after removing a wrong answer gives them an advantage: consistent switchers win twice as often as consistent non-switchers. So it's actually the exact opposite of what you're saying.

EDIT:

Could anyone write a simulation?

Simulation of what? You can only simulate behaviors that have a model, like the trajectory of a ball being thrown in a Newtonian universe. You can't simulate distributions of characteristics on a sample, but you can extrapolate quantities based on ratios (for example, if there's 55% of women, there's likely to be 270 men in a random sample), but that's what's being asked in the first place.

[Zykker]

@Helios

Im not denying that its retarded but for the question that Albatross asked, 0 is the answer.... unfortunately.