SOLUTION: A production line manufactures light bulbs with a defective rate of 0.05. What is the probability that in a batch of 20 light bulbs, 2 or more of them are defective? What is the pr

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Question 446473: A production line manufactures light bulbs with a defective rate of 0.05. What is the probability that in a batch of 20 light bulbs, 2 or more of them are defective? What is the probability that 1 or 2 bulbs are defective in the batch?
Answer by ewatrrr(24785) About Me  (Show Source):
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Hi,



A production line manufactures light bulbs with a defective rate of 0.05. What is P(in a batch of 20 light bulbs, 2 or more of them are defective)?



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 = .05  and q = .95

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

P(2 or more defective) = 1 - P(none) - P(one) 

                       = 1 -(.95)^20 - 20(.05)^1*(.95)^19

                       = 1 - .3585 - .3774 = .2641

P( 1 or 2 are defective) = .3774 + .1887 = .5661