Question: A transmitter is receiving a digital text, i.e., a sequence of digits. Suppose that each digit in the sequence is equally likely to be any

A transmitter is receiving a digital text, i.e., a sequence of digits. Suppose that each digit in the sequence is equally likely to be any number from 0 to 9, and the digits are appearing independently from each other. Each digit is transmitted correctly with probability p; and with probability q = 1− p, it is replaced by another digit with equal probabilities due to noise. Suppose an output sequence is “0,1.” What is the probability that, as a matter of fact, it was “0,0”?

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