Random events are events that do not have a determined outcome. The set of possible outcomes for a random event is always greater than one item.
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Mode is the most frequently occurring value in a data set. See related link. Note that in statistics, the definition is related to the data collected. In probability, the definition is related to the probability distribution which describes the random variable.
There are a number of definitions. In mathematics, it depends on the context that the word is used. One definition is for a "random event" where all outcomes are equally likely to occur. A random selection of lottery numbers means that in the long run, no one number is likely to occur more than another one. Random events are typically considered independent random events, in that one event can not affect the outcome of another one. A "random variable" means that the probability of any value occurring corresponds to a given probability distribution function. There is a common use of random, which means to act without a plan. See related link
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In math, the definition of a location is a point. A point gives a specific position or location on a plane surface.
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