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e. In probability theory, an event is a set of outcomes of an experiment (a subset of the sample space) to which a probability is assigned. [ 1] A single outcome may be an element of many different events, [ 2] and different events in an experiment are usually not equally likely, since they may include very different groups of outcomes. [ 3]
Mathematics is a field of study that discovers and organizes methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study ...
Borel–Cantelli lemma. In probability theory, the Borel–Cantelli lemma is a theorem about sequences of events. In general, it is a result in measure theory. It is named after Émile Borel and Francesco Paolo Cantelli, who gave statement to the lemma in the first decades of the 20th century. [ 1][ 2] A related result, sometimes called the ...
According to Winskel's definitions, a configuration of an event structure is a subset of all of whose finite subsets are consistent and whose events are all secured. Here, an event is secured when it belongs to a finite sequence of events from the configuration, each of which is enabled by the subset of earlier events from the same sequence. [1]
Subtraction is an operation that represents removal of objects from a collection. [ 1] For example, in the adjacent picture, there are 5 − 2 peaches—meaning 5 peaches with 2 taken away, resulting in a total of 3 peaches. Therefore, the difference of 5 and 2 is 3; that is, 5 − 2 = 3.
A typical sequence of secondary-school (grades 6 to 12) courses in mathematics reads: Pre-Algebra (7th or 8th grade), Algebra I, Geometry, Algebra II, Pre-calculus, and Calculus or Statistics. However, some students enroll in integrated programs [3] while many complete high school without passing Calculus or Statistics.
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