SOLUTION: A company receives a shipment of 16 items. A random sample of 4 items is selected , and the shipment is rejected if any two of these items proves to be defective. What is the proba

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Question 1193319: A company receives a shipment of 16 items. A random sample of 4 items is selected , and the shipment is rejected if any two of these items proves to be defective. What is the probability of accepting a shipment containing 4 defective items ?
Answer by ikleyn(52802) About Me  (Show Source):
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A company receives a shipment of 16 items. A random sample of 4 items is selected,
and the shipment is rejected if any two of these items proves to be defective.
What is the probability of accepting a shipment containing 4 defective items ?
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The probability that the shipment will be  highlight%28highlight%28accepted%29%29  is equal to the probability to find 0 or 1 
defective items in the random sub-set of 4 (four) items in the set of 16 items.


The number of all possible quadruples of 16 items is  C%5B16%5D%5E4 = %2816%2A15%2A14%2A13%29%2F%281%2A2%2A3%2A4%29 = 1820.

The number of all possible quadruples of the form (0 defective,4 good) is  C%5B4%5D%5E0%2AC%5B12%5D%5E4 = 1*495 = 495. 

The number of all possible quadruples of the form (1 defective,3 good) is  C%5B4%5D%5E1%2AC%5B12%5D%5E3 = 4*220 = 880.

So the probability that the shipment will be accepted is

    P = %28495+%2B+880%29%2F1820 = 1375%2F1820 = 275%2F364 = 0.755494505 = 75.55%  (rounded).    ANSWER

Solved.