I characterise probability statements as derived hypotheses (or predictions) about sequence of events. (They do not establish any laws or predictions about the properties of individual events, but rather laws or predictions about the properties of sequences of events.) This constitues their distinguishing feature.
In order to underscore the fact that the special character of probability statements must also be deducible from the character of the assumptions, I have stressed that these statements are derived hypotheses. We can only appreciate that which is important about probability statements when we understand what typifies their assumptions.
The typical features of these assumtions are characterised: (1) by the fact that the assumptions known to us (natural laws and special conditions [« initial conditions »]) are not sufficient for the deduction of a prediction about an individual element in the sequence of events; (2) by the fact that we cannot formulate a law for the missing conditions; from this we infer the proposition that these randomly changing conditions partly compensate each other (if, as it were, a plurality of evens gives them the opportunity of doing so); so that the sequence of events rather than its individual elements can be assumed to be partly independent « of the conditions about which we have no detailed knowledge ». (p. 151)
Popper, K. (2012). The two fundamental problems of the theory of knowledge. London: Routledge Classics. (Originally published 1978)