The informal aspects, arising in the interpretation of physical experiments, of the theory of probability and mathematical statistics are discussed. The conditions that verifying experiments must satisfy are presented and the role of heuristic (extralogical) assertions is analyzed using the example of mathematical expectation. The principal hypotheses implicit in experiments are enumerated: the principle of reproducibility (``the past will be repeated in the future''); the principle of reasonable sufficiency; and, the statistical principle (``better to predict something rather than nothing''). Considerable attention is devoted to Fisher and multisample confidence intervals. It is noted that Fisher confidence intervals are inconsistent. The arguments for introducing contrivances into practical calculations of probabilities are enumerated: incompleteness of any system of hypotheses; subjective estimates of probabilities; adjoining of statistical ensembles; nonstationariness and instability; rare phenomena; and, the use of classical probabilities and the law of large numbers. It is concluded that the relative frequency of appearance (empirical probability) is a ``normal'' physical quantity in the sense that it admits physical measurement. Its ``abnormality'' is manifested in the fact that it is burdened, more than other physical quantities, with conventions and hypotheses which must be specially checked (verified).