A binary communication channel carries data as one of two types of signals denoted by 0 and 1. Owing to noise, a transmitted 0 is sometimes received as a 1 and a transmitted 1 is sometimes received as a 0. For a given channel assume a probability of 0.94 that a transmitted 0 is correctly received as a 0 and a probability 0.91 that a transmitted 1 is received as a1. Further assume a probability of 0.45 of transmitting a 0. If a signal is sent. Determine:

a. Probability that a 1 is received
b. Probability that a 0 is received
c. Probability that a 1 was transmitted given that a 1 was received
d. Probability that a 0 was transmitted given that a 0 was received
e. Probability of an error