Coded mesages are sent during wartime using Morse code that

Coded mesages are sent during wartime using Morse code that uses \"DOTS\" and \"DASHES\" which are known to occur in the proportion 7:8, that is:

P(DOT sent) = 7/15 and P(DASH sent) = 8/15

However there is interference on the transmission line causing errors in the receiving transmission. Thus,

P(DASH received given that DOT sent) = 1/9 and P(DOT received given that DASH was sent) = 2/9.

Use Bayes\' Theorem to find that probability that DOT received was indeed sent as a DOT. That is, find P(DOT sent given that DOT is received).

Solution