A binary code (0,1) is transmitted along a noisy communication channel. In the absence of noise, relays A,B of the receiver are activated. If 0,1 are received respectively as a result of noise distortions, relay A may also be activated by a 1 and relay B by a 0.
The Probability of the appearance of 0 is 5/8(or 1-3/8). The statistical properties of the noise are such that 2/5 of the 0 and 1/3 of the 1 symbols are distorted.
Determine:
a. The probability that the true signal is 0 if relay A is activated?
b. The probability that the true signal is 1 if relay B is activated?