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Marcocapelle (talk | contribs) removed Category:Probability theory; added Category:Conditional probability using HotCat |
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Normally we define the '''conditional probability''' of an event ''A'' given an event ''B'' as:
:<math>P(A|B)=\frac{P(A\cap B)}{P(B)}.</math>
The difficulty with this arises when the event ''B'' is too small to have a non-zero probability. For example, suppose we have a [[random variable]] ''X'' with a [[uniform distribution (continuous)|uniform distribution]] on <math>[0,1],</math> and ''B'' is the event that <math>X=2/3.</math> Clearly, the probability of ''B,'' in this case, is <math>P(B)=0,</math> but nonetheless we would still like to assign meaning to a conditional probability such as <math>P(A|X=2/3).</math> To do so rigorously requires the definition of a regular conditional probability.
==Definition==
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