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 .

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step-by-step explanation:

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15