In some contexts, probabilistic argument means any argument involving probability theory.
In some contexts, it means a method of non-constructive existence proof in mathematics called the probabilistic method.
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For example, an argument by counsel consists of a presentation of the facts or evidence and the inferences that may be drawn therefrom, which are aimed at persuading a judge or jury to render a verdict in favor of the attorney's client.
An attorney may begin to develop an argument in the opening statement, the initial discussion of the case in which the facts and the pertinent law are stated.
In most cases, however, an attorney sets forth the main points of an argument in the closing argument, which is the attorney's final opportunity to comment on the case before a judge or jury retires to begin deliberation on a verdict.