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 %.

Difficulty level: Easy task (using definitions and simple reasoning)
Routine calculation training
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