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However, not all mutually exclusive events are collectively exhaustive. For example, the outcomes 1 and 4 of a single roll of a six-sided die are mutually exclusive (both cannot happen at the same time) but not collectively exhaustive (there are other possible outcomes; 2,3,5,6).
For example, events A and B are said to be collectively exhaustive if = where S is the sample space. Compare this to the concept of a set of mutually exclusive events. In such a set no more than one event can occur at a given time. (In some forms of mutual exclusion only one event can ever occur.)
The law of total probability is [1] a theorem that states, in its discrete case, if {: =,,, …} is a finite or countably infinite set of mutually exclusive and collectively exhaustive events, then for any event () = ()
Since and are mutually exclusive, the craps principle applies. For example, if the original roll was a 4, then the probability of winning is / / + / = This avoids having to sum the infinite series corresponding to all the possible outcomes:
To qualify as a probability distribution, the assignment of values must satisfy the requirement that if you look at a collection of mutually exclusive events (events that contain no common results, e.g., the events {1,6}, {3}, and {2,4} are all mutually exclusive), the probability that any of these events occurs is given by the sum of the ...
The worst of the pandemic appears to be behind us, and Americans are back to attending in-person events in droves. Going to a wedding or a dance party is one thing, but what about the Met Gala or ...
In probability theory, an outcome is a possible result of an experiment or trial. [1] Each possible outcome of a particular experiment is unique, and different outcomes are mutually exclusive (only one outcome will occur on each trial of the experiment).
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