Newbie: Difference between the meaning for the data analysis: proportion of correct responses and probability of correct responses Very newbie, sorry if the question seems to be not very smart...
If proportion of correct respones is defined as
Number of hits + Number of correct rejections / Number of trials
Is the probability of correct responses  -> probability of hits + probability of correct rejections / probability of all trials happening
-> Does the difference lie in the fact, that the probability uses distributions with the data of proportions? Is therefore probability of correct more important for data analysis?
-> Or is prob. and prop. the same thing?
-> And what does then "accuracy" mean? Prob. or prop.?

The difference between probability and proportion is that a proportion is over a finite number of given trials, while a probability is theoretical. The two are related in that if the probability of a miss is 5%, then over a larger and larger sample the miss count will come closer and closer to 5%.
A proportion computed over a large sample will give you a fair idea of the associated probability, a phenomenon that can be quantified by the computation of a Confidence Interval.
Accuracy in your context means the probability to make the correct decision (whatever this decision has to be, accept or reject). The "proportion" version of it being given by the formula (number of correct decisions made) / (total number of trials). Source: https://en.wikipedia.org/wiki/Accuracy_and_precision#In_binary_classification
See also: https://en.wikipedia.org/wiki/Receiver_operating_characteristic
