A communication system sends binary data {0 or 1} which is then detected at the receiver. The receiver occasionally makes mistakes and sometimes a 0 is sent and is detected as a 1 or a 1 can be sent and detected as a 0. Suppose the communication system is described by the following set of conditional probabilities:
(a) Assuming 0s and 1s are equally likely to be transmitted (i. e.Pr (0 transmitted) = 1/2 and Pr (1 transmitted) = 1/2), find Pr (0 received and Pr (1 received).
(b) Suppose a 0 is detected at the receiver. What is the probability that the transmitted bit was actually a 1? Also, if a 1 was detected at the receiver, what is the probability that the transmitted bit was actually a 0?
(c) What is the probability that the detected bit is not equal to the transmitted bit. This is the overall probability of error of the receiver.