SOLUTION: In a shipment of 20 smartphones, 2 are defective. How many ways can a quality control inspector randomly test 4 smartphones, of which 2 are defective?

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Question 1173046: In a shipment of 20 smartphones, 2 are defective. How many ways can a quality control inspector randomly test 4 smartphones, of which 2 are defective?
Answer by ikleyn(52879) About Me  (Show Source):
You can put this solution on YOUR website!
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Every time, the inspector adds 2 good smartphones to 2 defective.


He can select 2 good smartphones from the 18 good smartphones in  C%5B18%5D%5E2 ways = %2818%2A17%29%2F2 = 9*17 = 153 ways.


It is the number of all possible favorable quadruples.


The number of all possible quadruples is, meanwhile,  C%5B20%5D%5E4 = %2820%2A19%2A18%2A17%29%2F%281%2A2%2A3%2A4%29 = 4845.


THEREFORE, the probability under the problem's question is


    P = favorable%2Ftotal = C%5B18%5D%5E2%2FC%5B20%5D%5E4 = 153%2F4845 = 3%2F95 = 0.03157895.    ANSWER

Solved.