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

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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sweererlirumeX
Step 1
Here, X denotes that the item is defective, which follows binomial distribution with $n=4ZKS\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}PSKp=0.03$.
The formula to find the binomial probability is,
$P\left(X=x\right){=}^{n}{C}_{x}{p}^{x}{\left(1-p\right)}^{\left(n-x\right)}$
Step 2
Probability that at least one will have a defect:
The probability that at least one will have a defect is,
$P\left(X\ge 1\right)=1-P\left(X=0\right)$
$=1{-}^{4}{C}_{0}{\left(0.03\right)}^{0}{\left(1-0.03\right)}^{\left(4-0\right)}$
$=1-0.8853$
$=0.1147$
The probability that at least one will have a defect is 0.1147.