Question 1042591: In a shipment of 190 items, 3 are found defective. If 3 items are selected at random, what is the probability the shipment will be rejected if 1 of the 3 is defective?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! This is 1 of the 3, not at least 1 of the three, I am assuming.
3 ways 1 of the 3 can be defective, the first, second, or third.
3*(3/190)*(187/189)(186/188); the 3 takes care of the possibility the second is defective (187/190)(3/189)(186/188) and the third is defective (187/190)(186/189)(3/188). The denominators and numerators are the same but ordered differently.
The probability is 3*3*187*186/190*189*188=
313038/67510180=0.0464.
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a check would be along the lines that about 1/63 is defective, and 3 chances of doing that are 3/63, which is 1/21, of just under 5%, which fits with the answer.
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