ELEC 471 Class Exercise

In a digital communication system, messages are encoded into binary symbols 0 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 1 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.

Hint: Draw a tree diagram.

a.

What is the probability that a received 0 was transmitted as a 0?

b.

What is the probability that a received 1 was transmitted as a 1?

c.

What is the probability that any symbol is received in error?