In the digital signal transmission, due to noise, the received signals may be di

Question

In the digital signal transmission, due to noise, the received signals may be different from the signals sent out.  Suppose the transmitter sends out signal "0" with probability 0.7, and "1" with probability 0.3.  When "0" is transmitted, the receives receives "0" with probability 0.8, and "1" with probability 0.2.  When "1" is transmitted, the receiver receives "0" with probability 0.1, and "1" with probability 0.9.  Find the probability of error, i.e. the probability that "1" is received when "0" was transmitted or "0" is received when "1" was transmitted.

Explanation / Answer

Given P(0 transmitted)=0.7           P(1transmitted)=0.3           P(0 received| 0 transmitted)=0.8           P(1 received| 0 transmitted)=0.2           P(0 received| 1 transmitted)=0.1           P(1 received| 1 transmitted)=0.9 P(error)=P(1 received | 0 transmitted)*P(0 transmitted) + P(0received | 1 transmitted)*P(1 transmitted) =0.2*0.7 + 0.1*0.3 =0.17

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