SOLUTION: A shipment of 102 laptops contains 10 defective laptops. A quality control specialist chooses a sample of 8 laptops from the shipment. a) How many possible choices of 8 laptops

Question 1135509: A shipment of 102 laptops contains 10 defective laptops. A quality control specialist chooses a sample of 8 laptops from the shipment.
a) How many possible choices of 8 laptops can be made?
b) How many of these possible selections will not contain any defective laptops?
c) How many of the possible selections will contain at least one defective laptop?
d) How many of the possible selections will contain exactly one defective laptop?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
a is 102!/94!8! or 102C8=2.19 x 10^11 (2192950683 x 10^11) ANSWER a
No defective ones
92/102*91/101*90/100*89/99*88/98*87/97*86/96*85/95=0.4245 probability that none is defective so a 0.5755 probability at least one is defective.
1-(92C8/102C8)=1.2621418 x 10^11 ANSWER c, at least one defective
That means 9.308088718 x 10^10 ways there are no defective ones ANSWER b
exactly one is 10C1*92C7/102C8= 0.39948 probability or 8.76056 x 10^10 ways ANSWER d
Notice how the top part of the "choose" factor (hypergeometric distribution) adds to 102 and the bottom adds to 8.

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