Light bulbs
Task number: 3548
A merchant has decided to return a large shipment of light bulbs if a randomly chosen sample of ten light bubs contains more than one defective bulb.
What is the probability that he will return the shipment if the defect rate is 10 %?
Solution
The random variable \(X\) representing the number of defective bulbs has a binomial distribution with parameters \(n=10\), \(p=0{,}1\).
So \(P[X<2]=P[X=0]+P[X=1]=\binom{10}{0}(1-p)^{10}+\binom{10}{1}(1-p)^9p \doteq 0{,}349+0{,}387=0{,}736\).
Answer
The probability of rejecting the shipment is approximately 26 %.
