I was damned confused! I think I understand it now, so I'd like to share how to resolve this "paradox". First, to recap, suppose you have a process / experiment that produces a confidence interval [x, y], for which you say, if we repeat this experiment a lot of time, 95% of the cases we'll see that the [x, y] covers something that we are estimating, e.g. the true mean. We call this 95% Confidence Interval (CI) for the true mean. But then, your instructor, or the author of the book you are reading, will immediately follow up by the statement "Be careful! It's wrong to say that the CI you computed has 95% chance of containing the true mean". Confusion ensues. You lose sleep, you don't eat as much. Your parents, friends, and loved ones start to get worried because you don't look so well. You, on the other hand, has lost all confidence in your understanding of statistics and basics of probabilities. WHY on earth?? If 95% of the CIs produced by the re