Amessage source m of a digital communication system outputs a word of length 8 characters, with the characters drawn from the ternary alphabet {0,1,2}, and all such words are equally probable. what is the probability that m produces a word that looks like a byte (i. e., no appearance of ‘2’)?

The probability that M produces a word that looks like a byte is .

Step-by-step explanation:

It is given that a message source M of a digital communication system outputs a word of length 8 characters.

The characters drawn from the ternary alphabet {0,1,2}, and all such words are equally probable.

Total possible outcomes is

We need to find the probability that M produces a word that looks like a byte (i.e., no appearance of ‘2’). It means only 0 and 1 are included in the word.

Total favorable outcomes is

The formula for probability is

Therefore the probability that M produces a word that looks like a byte is .