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Chansondoree (talk | contribs) →Use in inference Example: make this a subsection of "Use in inference" |
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The wording "evidence" or "information" is generally used in the [[Bayesian probability|Bayesian interpretation of probability]]. The conditioning event is interpreted as evidence for the conditioned event. That is, ''P''(''A'') is the probability of ''A'' before accounting for evidence ''E'', and ''P''(''A''|''E'') is the probability of ''A'' after having accounted for evidence ''E'' or after having updated ''P''(''A''). This is consistent with the frequentist interpretation, which is the first definition given above.
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When [[Morse code]] is transmitted, there is a certain probability that the "dot" or "dash" that was received is erroneous. This is often taken as interference in the transmission of a message. Therefore, it is important to consider when sending a "dot", for example, the probability that a "dot" was received. This is represented by: <math>P(dot \ sent \mid dot \ received) = P(dot \ received \mid dot \ sent) \frac{P(dot \ sent)}{P(dot \ received)}.</math> In Morse code, the ratio of dots to dashes is 3:4 at the point of sending, so the probability of a "dot" and "dash" are <math>P(dot \ sent) = \frac {3}{7} \ and \ P(dash \ sent) = \frac {4}{7}</math>. If it is assumed that the probability that a dot is transmitted as a dash is 1/10, and that the probability that a dash is transmitted as a dot is likewise 1/10, then Bayes's rule can be used to calculate <math>P(dot \ received)</math>.
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