Changes fit inside the margin of error. Do they tell anything?

All the cool kids are Bayesians I. And I want to be too. I tried to read the article I'm linking to about a year ago, but then gave up, I'm not very persistent. But now I have a question, that I can't answer:

There are two containers: container A and container B. Each contain 1 million balls (not that it necessarily matters). From each 1000 random balls are taken. Of the thousand balls from container A 205 were red. From 1000 balls from container B 213 were red. After counting we put all the balls back into the container of their origin.

Then we repeat i.e. take thousand random balls from each container. How likely it is that also this time the sample from container B contains more red balls than the sample from container A?

I'm wondering this because finnish tweeter Mediakritiikki was confused by how the journalists don't know statistics, because there was a news article about poll in which all the changes in the results of how popular the parties are fit in to the margin of error, which was 2% in this case. I have complained about the same thing. But of course small changes mean something, but how much. And that I'm trying to find out with my question.

I feel handicapped because my lack of understanding of bayesian theorem, statistics and programming. I need some sort of help-line where I could talk to a mathematics or statistics teacher and get something cleared or at least some directions where to find the answers. I wanted to write a python program which would have had created similar situations, that I could have bet on, to see if I understand anything.

One way I would approach this is by finding out the confidence level, that I could have with such small differences with same sample size. But I don't think that is fruitful. I bet there is a simple answer. If someone could tell me how to get there I would be grateful.