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A manufacturing machine has a 2% defect rate. If 6 items are chosen at random, what...

A manufacturing machine has a 2% defect rate. If 6 items are chosen at random, what is the probability that at least one will have a defect?

Math   Statistics-And-Probability   
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Answer #1

A manufacturing machine has a 2% defect rate means that the probability that a randomly chosen item is defective is 0.02.

Let X be the number of defective items out of 6 items chosen at random. X has a Binomial distribution with parameters, number of trials n=6 and success probability (probability that the item is defective) p=0.02.

The probability that X=x items are defective, out of 6 items is

the probability that at least one will have a defect is same as the probability that X>=1

ans: the probability that at least one will have a defect is 0.1142

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