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Digital data are transmitted as a sequence of signals that represent 0s or 1s. Suppose that such data are being transmitted to a satellite and then relayed to a distant site. Suppose that due to electrical interference in the atmosphere, there is a 1-in-1000 chance that the transmitted 0 will be reversed between the sender and the satellite (i.e. distorted to the extent that the satellites receiver interprets the 0 as a 1) and a 2-in-1000 chance that a transmitted 1 will be reversed. Suppose that 40% of the transmitted digits are 0s.
a. What is the probability that a transmitted digit is correctly received by the satellite?
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