A binary communication system uses redundant transmission of bits to detect tran

Question

A binary communication system uses redundant transmission of bits to detect transmission errors. The

transmitter sends each bit twice. The receiver knows that a transmission error has occurred if the two

bits it receives are not the same. Assume the correct reception of any bit is independent from the

correct reception of any other bit. If the probability of each bit being correctly received is

p=0.9, what is the probability that the receiver will detect a transmission error given that at least one of the

bits is incorrect?

Please explain answer thanks.

Explanation / Answer

B = correct transmission of bit
P[exactly one bit incorrect] = P[BB'] + P[B'B] = 2*0.9*0.1 = 0.18
P[both bits incorrect] = 0.1*0.1 = 0.01

P[detect transmission error | at least 1 bit incorrect]
= 0.18/(0.18+0.01) = 18/19, ? 0.9474 <-------

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