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?

Respuesta :

Answer:

The appropriate answer is "0.0043".

Explanation:

The given values is:

Error probability,

p = 0.01

Received digits,

n = 10

and,

[tex]x\sim Binomial[/tex]

As we know,

⇒  [tex]P(x)=\binom{n}{x}p^xq^{n-x}[/tex]

Now,

⇒  [tex]P(x >1) =1- \left \{ P(x=0)+P(x=1) \right \}[/tex]

⇒                 [tex]=1-\left \{\binom{10}{0}(0.01)^0(0.99)^{10-0}+\binom{10}{0}(0.01)^1(0.99)^{10-1} \right \}[/tex]

⇒                 [tex]=1-0.9957[/tex]

⇒                 [tex]=0.0043[/tex]