probability is defined as the chance that a given event will occur.
probability is defined as the chance that a given event will occur.
which term is defined as the chance that a given event will occur?
probability
in order to avoid paradoxes (such as the borel's paradox), the following important distinction should be taken into account. if a given event is of nonzero probability then conditioning on it is well-defined (irrespective of any other events), as was noted above. by contrast, if the given event is of zero probability then conditioning on it is ill-defined unless some additional input is provided. wrong choice of this additional input leads to wrong conditional probabilities (expectations, distributions). in this sense, ""the concept of a conditional probability with regard to an isolated hypothesis whose probability equals 0 is inadmissible."" (kolmogorov.
conditioning (probability)
all observers will agree that for any given event, an event within the given event's future light cone occurs "after" the given event. likewise, for any given event, an event within the given event's past light cone occurs "before" the given event. the before-after relationship observed for timelike-separated events remains unchanged no matter what the reference frame of the observer, i.e. no matter how the observer may be moving. the situation is quite different for spacelike-separated events. fig. 2‑4 was drawn from the reference frame of an observer moving at from this reference frame, event c is observed to occur after event o, and event b is observed to occur before event o. from a different reference frame, the orderings of these non-causally-related events can be reversed. in particular, one notes that if two events are simultaneous in a particular reference frame, they are "necessarily" separated by a spacelike interval and thus are noncausally related. the observation that simultaneity is not absolute, but depends on the observer's reference frame, is termed the relativity of simultaneity.
spacetime