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In probability theory, conditional dependence is a relationship between two or more events that are dependent when a third event occurs. [1] [2] For example, if and are two events that individually increase the probability of a third event , and do not directly affect each other, then initially (when it has not been observed whether or not the ...
Events A and B can be assumed to be independent i.e. knowledge that A is late has minimal to no change on the probability that B will be late. However, if a third event is introduced, person A and person B live in the same neighborhood, the two events are now considered not conditionally independent.
In mathematics, a function is a rule for taking an input (in the simplest case, a number or set of numbers) [5] and providing an output (which may also be a number). [5] A symbol that stands for an arbitrary input is called an independent variable, while a symbol that stands for an arbitrary output is called a dependent variable. [6]
The gambler's fallacy, also known as the Monte Carlo fallacy or the fallacy of the maturity of chances, is the belief that, if an event (whose occurrences are independent and identically distributed) has occurred less frequently than expected, it is more likely to happen again in the future (or vice versa).
Any combination of events using the operations and, or, and not is also an event, and assigning probabilities to all outcomes generates a probability for every event. In technical terms, this means that the set of events and the three operations together constitute a Boolean algebra of sets, with an associated probability function .
An event, however, is any subset of the sample space, including any singleton set (an elementary event), the empty set (an impossible event, with probability zero) and the sample space itself (a certain event, with probability one). Other events are proper subsets of the sample space that contain multiple elements. So, for example, potential ...
A probability is a way of assigning every event a value between zero and one, with the requirement that the event made up of all possible results (in our example, the event {1,2,3,4,5,6}) is assigned a value of one. To qualify as a probability, the assignment of values must satisfy the requirement that for any collection of mutually exclusive ...
event A subset of the sample space of a procedure or experiment (i.e. a possible outcome) to which a probability can be assigned. For example, on rolling a die, "getting a three" is an event (with a probability of 1 ⁄ 6 if the die is fair), as is "getting a five or a six" (with a probability of 1 ⁄ 3).