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Mutually Exclusive Events


Mutually exclusive events are events in a common probability space that are pairwise disjoint. For n such events,

 X_i intersection X_j=emptyset

whenever i!=j, where emptyset is the empty set. Consequently, the conditional probability satisfies P(X_i|X_j)=0 for i!=j whenever P(X_j)>0. When P(X_j)=0, the usual ratio definition of conditional probability does not assign a value (Grinstead and Snell 2006, pp. 134-135).


See also

Disjoint Sets, Event

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References

Grinstead, C. M. and Snell, J. L. Introduction to Probability. CHANCE Project version, July 4, 2006. https://math.dartmouth.edu/~prob/prob/prob.pdf.

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Mutually Exclusive Events

Cite this as:

Weisstein, Eric W. "Mutually Exclusive Events." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/MutuallyExclusiveEvents.html

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