Consider a binary communication channel, where 0 or 1 is sent independently over time with probability p0=0.6 and p1=0.4

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Consider a binary communication channel, where 0 or 1 is sent
independently over time with probability p0=0.6 and p1=0.4,
respectively, and the noisy channel introduces errors independently
over time with probabilities p01=P(1 is received | 0 is sent)=0.2
and p10=P(0 is received | 1 is sent)=0.1.
(a) Calculate the probability that “01” is sent.
(b) Calculate the probability that “01” is received.
(c) Calculate the probability that “01” is sent given that “01”
is received.
(d) Is the event that “01” is sent independent of that “01” is
received? Justify your answer.