``Although particle physicists may use the words `confidence interval' loosely, the most common meaning is still in terms of original classical concept of ``coverage'' which follows from the method of construction suggested in Fig. ... This concept is usually stated (too narrowly, as noted below) in terms of a hypothetical ensemble of similar experiments, each of which measures and computes a confidence interval for with say, 68% C.L. Then the classical construction guarantees that in the limit of a large ensemble, 68% of the confidence intervals contain the unknown true value , i.e., they `cover' . This property, called coverage in the frequentistic sense, is the defining property of classical confidence intervals. It is important to see this property as what it is: it reflects the relative frequency with which the statement, ` is in the interval ', is a true statement. The probabilistic variables in this statements are and ; is fixed and unknown. It is equally important to see what frequentistic coverage isnot: it is a not statement about the degree of belief that lies within the confidence interval of a particular experiment. The whole concept of `degree of belief' does not exist with respect to classical confidence intervals, which are cleverly (some would say devilishly) defined by a construction which keeps strictly to statements about andneveruses a probability density in the variable .

I think that the reader can judge for himself whether this approach seems reasonable. From the Bayesian point of view, the full answer is provided by , to use the same notation of Ref. [68]. If this evaluation has been carried out under the requirement of coherence, from one can evaluate a probability for to lie in the interval . If this probability is , in order to stick to the same value this implies:This strict classical approach can be considered to be either a virtue or a flaw, but I think that both critics and adherents commonly make a mistake in describing coverage from the narrow point of view which I described in the preceeding paragraph. As Neyman himself pointed out from the beginning, the concept of coverage is not restricted to the idea of an ensemble of hypothetical nearly-identical experiments. Classical confidence intervals have a much more powerful property: if, in an ensemble ofreal, different, experiments, each experiment measures whatever observables it likes, and construct a C.L. confidence interval, then in the long run of the confidence intervals cover the true value of their respective observables. This is directly applicable to real life, and is the real beauty of classical confidence intervals.''

- one believes that is in that interval;
- one is ready to place a bet on being in that interval and a bet on being elsewhere;
- if one imagines situations in which one has similar conditions (they could be different experiments, or simply urns containing a 68% proportion of white balls) and thinks of the relative frequency with which one expects that this statement will be true (), logic applied to the basic rules of probability imply that, with the increasing , it will become more and more improbable that will differ much from (Bernoulli theorem).