Question

A noisy transmission channel has a per-digit error probability p = 0.01.

(a) Calculate the probability of more than one error in 10 received digits?

Answer 1

The appropriate answer is "0.0043".

Step-by-step explanation:

The given values is:

Error probability,

p = 0.01

Received digits,

n = 10

and,

`x\sim Binomial`

As we know,

⇒
`P(x)=\binom{n}{x}p^xq^(n-x)`

Now,

⇒
`P(x >1) =1- \left \{ P(x=0)+P(x=1) \right \}`

⇒
`=1-\left \{\binom{10}{0}(0.01)^0(0.99)^(10-0)+\binom{10}{0}(0.01)^1(0.99)^(10-1) \right \}`

⇒
`=1-0.9957`

⇒
`=0.0043`