TU Wien:Statistik und Wahrscheinlichkeitstheorie UE (Bura)/Übungen 2019W/1.7

Coding

When coded messages are sent, there are sometimes errors in transmission. In particular, Morse code uses "dots" and "dashes", which are known to occur in proportion 3 : 4. Suppose there is interference on the transmission line, and with probability 1/8 a "dot" is mistakenly received as a "dash" and vice versa. If we receive a "dot", what is the probability that a "dot" was sent?

Lösungsvorschlag von Gittenburg

--Gittenburg 09:49, 15. Okt. 2019 (CEST)

             dot or dash
        3/7 /           \ 4/7
         dot           dash
    1/8 /   \ 7/8  1/8 /  \ 7/8
      dash      dot       dash

(3/7 * 7/8) / (3/7 * 7/8 + 4/7 * 1/8) = 0.84