Two prison inmates communicate in binary by tapping on the adjacent wall. Suppose that the probability of receiving a zero given that a zero was sent is 0.98, the probability of receiving a one given that a one was sent is 0.96, and the probability of sending a one is 0.6.
(a) If one is received, what is the probability that a zero was sent?
(b) If a single digit is sent, what is the probability that the opposite digit is received?
(c) If two digits are sent independently, what is the probability that both digits received are the ones that were sent?