This has to do with confidence intervals.
When you say something like 0.75 ± 0.15 with 99.9% probability what you mean to say is that on repeating the experiment many times, the range reported by the experiment (e.g. 0.75 ± 0.15) will contain the true population mean 99.9% of the time. Note that when the experiment is repeated the reported mean and its error may not be the same (they are a function of the data).
In other words, in repeated experiments, C% of confidence intervals will contain the true population mean.
The confidence interval (most commonly 95% CIs are used, by convention) is often misinterpreted as the probability that the population mean falls within the reported range. This is not strictly true, since the population mean is a constant and either does or does not fall within the range.
You would never use with 30% probability (although you can) because 30% is too low.
In polling data the verbiage is "19 times out of 20". For example, you might hear "75% ± 3 people agree, 19 times out of 20". This corresponds to a 19/20 = 0.95 (95%) confidence interval. In other words, if the same poll were to be repeated many many times, the population fraction of those who agree would be spanned by the interval 19/20 times.
The appropriate way to report such results is 0.75 ± 0.15 (95%CI).
I have a reasonably pedagogical column in Nature Methods (Points of Significance) about this very topic.