In a digital communication system messages are encoded in to

In a digital communication system, messages are encoded in to the 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 0.5 Further suppose that the probability of a transmitted 0 being received as a 1 is 0.05 and the probability of a transmitted 1 being received as a 0 is 0.08. Find the probability that that it was a 1 transmitted given that a 1 was received.

Solution

Probability of a depending events

Given probability of transmitting 0 as 0.5 thus we got probability of transmitting 1 is 0.5 P(A)=0.5 i.e transmitting 1.

probability of a transmitted 1 being received as a 0 is 0.08 thus probability of transmitted 1 being recieved as a 1 is 1-0. 08= 0.92 i.e P(B)

Two events P(A) and P(B) occurs thus P(A). P(B)= 0.5*0.92=0.46