Definition binomial probability:
\(\displaystyle{P}{\left({X}={k}\right)}={\left(\frac{{n}}{{k}}\right)}\cdot{p}^{{k}}{\left({1}-{p}\right)}^{{n}}-{k}\)

Complement rule:

PSKP(A^c)=P(not A)=1-P(A)

Solution

n=Number of trials = 100

p=Probability of success=\(\displaystyle\frac{{50}}{{100}}={0.05}\)

(50 out of 1000 page contains errors)

Evaluate the definition of binomial probability at k=0:

PSKP(X=0)=(100/0)*0.05^0(1-0.05)^100-0 =(100!/(0!(100-0)!))0.05^0*0.95^100 ~0.0059ZSK

Use the complement rule:

PSKP(X=>1)=1-P(X=0) =1-0.0059 =0.9941 =99.41%ZSK

Command \(\displaystyle{T}{i}\frac{{83}}{{84}}\)-calculator: 1-binimedf(100,0.05,0)

Complement rule:

PSKP(A^c)=P(not A)=1-P(A)

Solution

n=Number of trials = 100

p=Probability of success=\(\displaystyle\frac{{50}}{{100}}={0.05}\)

(50 out of 1000 page contains errors)

Evaluate the definition of binomial probability at k=0:

PSKP(X=0)=(100/0)*0.05^0(1-0.05)^100-0 =(100!/(0!(100-0)!))0.05^0*0.95^100 ~0.0059ZSK

Use the complement rule:

PSKP(X=>1)=1-P(X=0) =1-0.0059 =0.9941 =99.41%ZSK

Command \(\displaystyle{T}{i}\frac{{83}}{{84}}\)-calculator: 1-binimedf(100,0.05,0)