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In fact, the same result even holds in non-standard analysis—where infinitesimal probabilities are allowed. [ 5 ] Moreover, the event "the sequence of tosses contains at least one T {\displaystyle T} " will also happen almost surely (i.e., with probability 1).
Retrocausality, or backwards causation, is a concept of cause and effect in which an effect precedes its cause in time and so a later event affects an earlier one. [1] [2] In quantum physics, the distinction between cause and effect is not made at the most fundamental level and so time-symmetric systems can be viewed as causal or retrocausal.
Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes.Two events are independent, statistically independent, or stochastically independent [1] if, informally speaking, the occurrence of one does not affect the probability of occurrence of the other or, equivalently, does not affect the odds.
The flash of light is shown as the 45° red lines. The points at which the two light flashes hit the ends of the train are at the same level in the diagram. This means that the events are simultaneous. In the second diagram, the two ends of the train moving to the right, are shown by parallel lines.
In measure theory (a branch of mathematical analysis), a property holds almost everywhere if, in a technical sense, the set for which the property holds takes up nearly all possibilities. The notion of "almost everywhere" is a companion notion to the concept of measure zero , and is analogous to the notion of almost surely in probability theory .
Individual random events are, by definition, unpredictable, but if there is a known probability distribution, the frequency of different outcomes over repeated events (or "trials") is predictable. [note 1] For example, when throwing two dice, the outcome of any particular roll is unpredictable, but a sum of 7 will tend to occur twice as often ...
To qualify as a probability, the assignment of values must satisfy the requirement that for any collection of mutually exclusive events (events with no common results, such as the events {1,6}, {3}, and {2,4}), the probability that at least one of the events will occur is given by the sum of the probabilities of all the individual events. [28]
A logical fallacy of the questionable cause variety, it is subtly different from the fallacy cum hoc ergo propter hoc ('with this, therefore because of this'), in which two events occur simultaneously or the chronological ordering is insignificant or unknown. Post hoc is a logical fallacy in which one event seems to be the cause of a later ...