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.

Yulia

Yulia

Answered question

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.

Answer & Explanation

sovienesY

sovienesY

Skilled2020-12-18Added 89 answers

Definition binomial probability: P(X=k)=(nk)pk(1p)nk
Complement rule:
P(Ac)=P()=1P(A)
Solution
n=Number of trials = 100
p=Probability of success=50100=0.05
(50 out of 1000 page contains errors)
Evaluate the definition of binomial probability at k=0:
P(X=0)=(1000)0.050(10.05)1000=(100!0!(1000)!)0.0500.951000.0059
Use the complement rule:
P(X1)=1P(X=0)=10.0059=0.9941=99.41%
Command Ti8384-calculator: 1-binimedf(100,0.05,0)

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