A shipment of 10 items has two defective and eight nondefective items. In the inspection of the shipment, a sample of items will be selected and tested. If a defective item is found, the shipment of 10 items will be rejected.
If a sample of 3 items is selected, what is the probability that the shipment will be rejected?
I used f(x)=(nCr(2,x)*nCr(8,3-x))/nCr(10,3)
Book answer is .5333333.
Is the book right?
This is a hypergeometric problem! N=10 n1=2 and n2=8 and the Probability=1-(2C0)*(8C3)/(10C3). Because if one defective component is found, the shipment will be rejected. You only need to concern about there is no defective component is found, and then use 1 minus the answer. The book answer is correct.