An information source produces 0 and 1 with probabilities 0.3 and 0.7 respectively. The output of the source is transmitted via a channel that has probability of error (turning a 1 into 0 and 0 into 1) equal to 0.2.
a) what is the probability that a 1 is observed ?
b) What is the probability that a 1 was the output of the source if at the output of the channel a 1 is observed