Reference no: EM131754159

Question: In the serial transmission of a byte (such as over a modem) errors in each bit occur independently with probability Q. For every 8-bit byte sent, a parity check bit is appended so that each byte transmitted actually consists of 9 bits. The parity bit is chosen so that the group of 9 bits has "even parity," i.e., the number of 1's, is even. Errors can be detected by checking the parity of the received 9-bit sequence.

(a) What is the probability that a single error occurs?

(b) What is the probability that errors occur but are not detected? Write your answer as an expression involving the error probability Q.