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 \text{dot sent \mid} dot| \text{ dot received}) = P(\text{dot \ received \mid} dot| \text{ dot sent}) \frac{P(\text{dot \ sent})}{P(\text{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(\text{dot \ sent}) = \frac {3}{7} \ and \ P(\text{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(\text{dot \ received})</math>.
