SOLUTION: A manufacturing machine has a 1% 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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Question 443534: A manufacturing machine has a 1% defect rate.
If 4 items are chosen at random, what is the probability that at least one will have a defect?
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi

A manufacturing machine has a 1% defect rate. 

4 items are chosen at random

P(at least one will have a defect)

Note: The probability of x successes in n trials is: 

P = nCx* p%5Ex%2Aq%5E%28n-x%29 where p and q are the probabilities of success and failure respectively. 

In this case p = .01 and q = .99

nCx = n%21%2F%28x%21%28n-x%29%21%29

 P(at least one defective) = 1 - P(none defective) = 1 - (.99)^4 =.0394 

P(at least one defective)= .0394