A company Web site contains errors on 50 of 1000 pages. If 100 pages are sampled randomly, without replacement, approximate the probability that at least 1 of the pages in error are in the sample.

Question
Binomial probability
asked 2020-12-17
A company Web site contains errors on 50 of 1000 pages. If 100 pages are sampled randomly, without replacement, approximate the probability that at least 1 of the pages in error are in the sample.

Answers (1)

2020-12-18
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)
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