"In transmitting dot and dash signals, a communication system changes 1/4 of the dots to dashes and 1/3 of the dashes to dots. If 40% of the signals transmitted are dots and 60% are dashes, what is the probability that a dot received was actually a transmitted dot?"
Answer = 3/5
Hello, everyone,
I am having issues wording the events such that they fit coherently in Bayes' rule even though I am able to solve the problem mathematically. Could someone please give me an example of their wordings for the events?
Define $$A = \text{"A randomly selected transmitted signal is a dot"}$$ $$B = \text{"A randomly selected received signal is a dot"}$$
Then you have: $$p(\bar B|A) = 1/4$$ $$p(B|\bar A) = 1/3$$ $$p(A) = 0.4$$ $$p(\bar A) = 0.6$$
Now just apply Bayes' theorem to find $p(A|B)$.