Question

A message 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’)?

Answer 1

The probability that the message source produces a byte without the appearance of '2' is 0.003058.

Step-by-step explanation:

The probability that the message source produces a byte, which is a word without the appearance of '2', can be calculated by determining the number of possible words without '2' and dividing it by the total number of possible words.

The ternary alphabet {0,1,2} has 2 possible choices for each character since we want to exclude '2'.

Therefore, the probability is (2/3)^8 = 0.003058.

Answer 2

The probability that M produces a word that looks like a byte is
`((2)/(3))^8`.

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

`3* 3* 3* 3* 3* 3* 3* 3=3^8`

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

`2* 2* 2* 2* 2* 2* 2* 2=2^8`

The formula for probability is

`p=\frac{\text{Favorable outcomes}}{\text{Total outcomes}}`

`p=(2^8)/(3^8)`

`p=((2)/(3))^8`

Therefore the probability that M produces a word that looks like a byte is
`((2)/(3))^8`.