SOLUTION: The probability that a bolt is defective is 0.2%. Bolts are packed in boxes of 500. Two boxes are picked at random from the production line. Find the probability that one has two d

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Question 1183559: The probability that a bolt is defective is 0.2%. Bolts are packed in boxes of 500. Two boxes are picked at random from the production line. Find the probability that one has two defective bolts and the other has one defective bolts.
Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
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The probability that a bolt is defective is 0.2%. Bolts are packed in boxes of 500.
Two boxes are picked at random from the production line. Find the probability that
one has two defective bolts and the other has one defective bolts.
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    P = P%5B1%5D%2AP%5B2%5D + P%5B2%5D%2AP%5B1%5D


The probabilities  P%5B1%5D  and  P%5B2%5D  are the binomial distribution probabilities


    P%5B1%5D = 500%2A0.002%2A%281-0.002%29%5E499 = 0.368248.


    P%5B2%5D = %28%28500%2A499%29%2F2%29%2A0.002%5E2%2A%281-0.002%29%5E498 = 0.184124.


    P = 0.368248*0.184124 + 0.184124*0.368248 = 0.135607.    ANSWER

Solved.