A manufacturing machine has a 3% defect rate. If 4 items

Nann 2021-09-15 Answered
A manufacturing machine has a 3% defect rate.
If 4 items are chosen at random, what is the probability that at least one will have a defect?
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Expert Answer

sweererlirumeX
Answered 2021-09-16 Author has 91 answers
Step 1
Here, X denotes that the item is defective, which follows binomial distribution with n=4ZKSandPSKp=0.03.
The formula to find the binomial probability is,
P(X=x)=nCxpx(1p)(nx)
Step 2
Probability that at least one will have a defect:
The probability that at least one will have a defect is,
P(X1)=1P(X=0)
=14C0(0.03)0(10.03)(40)
=10.8853
=0.1147
The probability that at least one will have a defect is 0.1147.
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