SOLUTION: 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?

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.
-----------------------
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.
RELATED QUESTIONS
A shipment of 10 times has 2 defective and 8 non defective items. in the inspection of... (answered by Boreal)

A shipment of 10 items has two defective and eight nondefective items. In the inspection (answered by stanbon)

A shipment of 10 items has two defective and eight non defective units.In the inspection... (answered by ikleyn)

A shipment of 10 items has two defective and eight non defective units. In the inspection (answered by math_tutor2020)

A shipment of 10 items has two defective and eight non defective units. In the inspection (answered by CPhill,ikleyn,greenestamps)

A company receives a shipment of 16 items. A random sample of 4 items is selected , and... (answered by ikleyn)

A certain item is manufactured by 3 factories. Suppose we have a stockpile of the items... (answered by Boreal)

A company receives a shipment of 16 items. A random sample of 4 items is selected , and... (answered by ikleyn)