In a binary communication system, 1’s are sent twice as frequently as 0’s. Which
ID: 3071244 • Letter: I
Question
In a binary communication system, 1’s are sent twice as frequently as 0’s. Whichever
symbol is sent, the receiver makes the correct decision as to which it was only 3/4 of the
time. Errors in dierent symbol transmissions are independent.
(a) Suppose that the string of symbols 1001 is transmitted. What is the probability that
all symbols in the string are received correctly?
(b) Find the probability of an error being incurred as a result of the receiver making the
wrong decision.
(c) Find the conditional probability that a 0 was sent given that the receiver decided
that a 1 was sent
Explanation / Answer
a) suppose a string of symbols 1001 is transmitted. The probability that all strings are recived correctly is 1/64 = 0.015625
b) probability of an error being incurred as a result of the reciever making a wrong decision(in the above case) is 1 - 0.015625 = 0.984375
c) the conditional probability that a 0 was sent given that the receiver decided that a 1 was sent is : (1/3) * (1/4) = 1/12 ans