Talk:Puzzles/Statistical puzzles/3 Bags of Marbles/Solution

That's Just not True :-P
This is my take on this whole talk page... maybe I didn't understand the problem? Well this makes sense to me :)

-to random ip address guy

Your logic assumes that the concept of probability actually exists but it doesn't, it's just a mathematical concept to simplify the world. In actuality all things that happen always have a 100% chance of happening and all things that don't happen always have a 0% chance of happening. It's like watching a movie. The same events will always happen unless they are altered even before they can be predicted by probablity. No matter how much you rewind a movie, or even if you were rewinding time itself, the same events always happen. Now thinking of probability just as a mathematical concept certain things just happen more often that others and this is simplified into saying that there is a greater chance of such and such happening again. So if we took that random male voter from your example we could indeed say that there is a 55% chance he voted for Bush. Sure, at the end of the day he either did vote for him or he didn't but if you look at it that way probability is irrelevant and non-existant.

But anyway, I think the answer to this puzzle needs to be corrected. Correct me if I'm wrong but this is how I interpretted it: a marble is chosen randomly and it happens to be white and another marble is to be chosen from the same bag. We can eliminate bag 2 from the equation since that can't be the bag that we're concerned with. This means it's either bag 1 or 2. In bag 1 we will always choose a white marble because there are only white marbles, a 100% chance. In bag 3 we will always choose the black marble since if this is the bag at hand, the white marble was already removed, a 0% chance of choosing a white marble. So the average is a 50% chance of choosing a white marble. I'm not sure if you meant the white marble that's chosen is removed from the bag or replaced, if it's replaced the answer should be a 75% chance.

That got long, sorry if you read all that ^_^ thanks though. So did I get it?

--Swizzly 00:46, August 15, 2005 (UTC)

Correct me if I'm wrong, but the fact that you have picked a white marble does indeeed tell you that you have picked either bag 1 or bag 3.

Dear 205.196.132.147
Before vandalizing module like thi you should consult with others here, if you don't want module resumed to it's previous state. Thank you. --Divinity 10:06, 18 Jun 2005 (UTC)
 * if by any chance after reading comment you want to put "either 0.0 or 1.0" please don't. "0.0 or 1.0" is not a probability. It is the outcome. Probability indicates how often would this outcome happen. By saying probability is 2/3, we mean that if we pick a random bag and draw a white marble out of it 100 times, and after each event draw another one, ~67 of theese marbles will be white. *this* is the probability. --Divinity 05:31, 19 Jun 2005 (UTC)

Removed fallacious argument from main page
COMMENT: Once we get to the point described in the puzzle the probability that the second ball will be white is either 1.0 or 0. It can be nothing else.

Probability has to do with the situation PRIOR to an event. Once the outcome is determined probability is no longer a factor. In the case of the scenario presented by this puzzle, the outcome has already been determined. The fact that we don't know the color of the second ball doesn't change the fact that its color is fixed. That we don't see the color doesn't mean there is any chance that it can be different from what it is. Only one outcome is possible when the second ball if taken out of the bag.

It's true that if we were asking, before we started, what the probabilies are that we WOULD get certain outcomes the probability of getting bag, white ball, white ball is twice that of getting bag, white ball, black ball. But that's not the question asked by the puzzle. The puzzle says we've already selected a bag. That means the colors of both balls have been determined. If it happens to be the bag with one white and one black there's probability associated with different color outcomes just prior to selection of the first ball, but after that first ball is selected there is no subsequent possibility of different scenarios. Only one scenario is possible even if we don't know what that scenario is.

Here's another example: Exit polling data indicate that 55% of males who voted in the last election voted for Bush. So, before we do anything, we can say that if we randomly select a male who voted there's a 0.55 probability that it'll be somebody who voted for Bush.

But once we select the person, that person either voted for Bush or he didn't. If we say there's a 0.55 probability he voted for Bush, we are not being accurate. There are only two possibilities at that point. Either he voted for Bush (1.0) or he did not (0).

Same with flipping a coin. Before the coin is flipped you can say there's a 0.50 probability it'll be heads. If you say ahead of time that you're going to call heads there's a 0.50 probability that you'll be right. But once it's been flipped it is what it is. If you say heads you're either right or you're wrong. If the coin beneath the hand covering it is tails it is tails whether you can see that or not. If you say heads at that point your probability of being right is zero.