Question 653038: Suppose five items are selected randomly from a production line that is known to produce defective items 5% of the time. What is the probability of getting exactly two defective items?
Answer by Shana-D77(132)   (Show Source):
You can put this solution on YOUR website! Thankfully not 25%!
5% = 0.05
The P of getting one defect is 0.05 (1/20)
The P of getting one defect is 0.05 (1/20)
I wrote this twice because the second deflect doesn't depend on the first one, like flipping a coin.
The P of getting two defects is (1/20)(1/20) = 1/400 = .25%
Though (you'll hate me here) the fact that you already pulled one defect affects the P of getting another. It makes the second chance less. How much less will depend on how many items are on the line: If there are 100 items vs if there are 1,000 items, for example.
If there are only 100, the chance of getting 2 is:
(5/100)(4/99) = .202%
If there are 1,000, the chance of getting 2 is:
(50/1000)(49/999) = .245%
Since you have no information on how many objects are being produced in the factory, I'd go with .25%
:)
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