In a digital communication system messages are encoded into

In a digital communication system, messages are encoded into the binary symbols O.
and 1 . Because of noise · in the system, the incorrect symbol is sometimes received.
Suppose that the probability of a 0 being transmitted is 0.4 and the probability of a I
being transmitted is 0.6. Further suppose that the probability of a transmitted 0 being
received as a 1 is 0.08 and the probability of a transmitted 1 being received as a 0 is
0.05 . Find:
a) The probability that a received 0 was transmitted as a 0.
b) The probability that a received 1 was transmitted as a 1 .
c) The probability that any symbol is received in error.

Solution