A simple binary communication channel carries messages by using only two signals; say 0 and 1. We assume that, for a given binary channel, 40% of the time 0 is transmitted; the probability that a transmitted 0 is correctly received is 0.90 and the probability that a transmitted 1 is correctly received is 0.95. Determine (a) the probability of a 1 being received (b) given a 1 is received, the probability that a 0 was transmitted (c) given a 0 is received, the probability that a 0 was transmitted, (d) given a 0 is received, the probability that a 1 was transmitted.