SOLUTION: a company produce parts, a quality control worker picks 12 parts and rates them. two of them were defective, and 10 were fine. what is the probability that he randomly picks two de

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Question 1200474: a company produce parts, a quality control worker picks 12 parts and rates them. two of them were defective, and 10 were fine. what is the probability that he randomly picks two defective parts in a row? find the probability that at least one part is fine. find the probability that both parts are fine.
Answer by ikleyn(52779)   (Show Source): You can put this solution on YOUR website!
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a company produces parts, a quality control worker picks 12 parts and rates them.
two of them were defective, and 10 were fine.
(a) what is the probability that he randomly picks two defective parts in a row?
(b) find the probability that at least one part is fine.
(c) find the probability that both parts are fine.
~~~~~~~~~~~~~~~~~~~ 

The number of all possible pairs of 12 parts is   =  = 6*11 = 66.


(a)  Of these 66 different pairs, there is ONLY ONE PAIR consisting of two
     defective parts.

     THEREFORE, the probability to pick two defective parts at a time is  .    ANSWER



(b)  Again, there are 66 different pairs, in total, and only one pair
     contains two (both) defective parts.

     The rest, 66-1 = 65 pairs have AT LEAST one good part.


     THEREFORE, the probability to have at least one good part in a pair is  .    ANSWER



(c)  The number of pairs, having both good parts, is   =  = 5*9 = 45.

     THEREFORE, the probability that both parts are fine is   = .    ANSWER

Solved, with explanations.



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