A binary data source S produces 0's and l's independently with probabilities P(0) = 0.2 and P(1) = 0.8. These binary data are then transmitted over a noisy channel that reproduces a 0 at the output for a 0 in with probability 0.9, that is, P(0|0) = 0.9. The channel erroneously produces a 0 at its output for a 1 in with probability 0.2, that is, P(0|1)= 0.2. (a) Find P(1|0) and P(1|1). (b) Find the probability of a 0 being produced at the channel output. (c) Repeat part (b) for a 1. (d) If a 1 is produced at the channel output, what is the probability that a 0 was sent