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(52803)   (Show Source): You can put this solution on YOUR website!
.
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 ?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The probability that the shipment will be    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   =  = 1820.

The number of all possible quadruples of the form (0 defective,4 good) is   = 1*495 = 495. 

The number of all possible quadruples of the form (1 defective,3 good) is   = 4*220 = 880.

So the probability that the shipment will be accepted is

    P =  =  =  = 0.755494505 = 75.55%  (rounded).    ANSWER

Solved.



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