Probability 1

1. The simplest error detection scheme used in data communication is parity-checking. Usually messages
sent consist of characters, each character consists of a number of bits (a bit is the smallest
unit of information and is either 1 or 0). In parity-checking, a 1 or 0 is appended to the end of each
character at the transmitter to make the total number of 1’s even. The receiver checks the number of
1’s in every character received, and if the result is odd it signals an error. Suppose that each bit is
received correctly with probabaility 0.999, independently of other bits. What is the probability that
a 7-bit character is received in error, but the error is not detected by the parity check?


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