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anonymous
 5 years ago
In a factory there are three separate production lines which all produce the same type of CDplayer. Line A produces 30% of the CDplayers, line B produces 25% and line C 45%. In a quality inspection 2% of line A's players are faulty, in line B 3% are faulty and in line C 5%.
One CDplayer is picked at random. What is the probability that it is:
a) Faulty
b) It has been produced in line B when it is know that it is faulty?
Thank you for your help!
anonymous
 5 years ago
In a factory there are three separate production lines which all produce the same type of CDplayer. Line A produces 30% of the CDplayers, line B produces 25% and line C 45%. In a quality inspection 2% of line A's players are faulty, in line B 3% are faulty and in line C 5%. One CDplayer is picked at random. What is the probability that it is: a) Faulty b) It has been produced in line B when it is know that it is faulty? Thank you for your help!

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I believe that Venn diagram and Bayes' theorem are of use in this task.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0a) Faulty Using the law of total probability: P[Faulty] = P[FaultyFactory A]P[Line A] + P[FaultyLine B]P[Line B] + P[FaultyLine C]P[Line C] \[.02 \times .3 + .03 \times .25 + .05 \times .45\] .036 or 3.6% chance

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I believe that b) can now be solved using Bayes' theorem. Let F = faulty and B = line B. Now Bayes' theorem is: \[P(BF)=(P(B)P(FB))/P(F)\] Plug in the values we allready have we get: \[P(BF)=(0.25\times0.03)/0.036\] \[P(BF)\approx0.21\]
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