anonymous
  • anonymous
In a factory there are three separate production lines which all produce the same type of CD-player. Line A produces 30% of the CD-players, 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 CD-player 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!
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
I believe that Venn diagram and Bayes' theorem are of use in this task.
anonymous
  • anonymous
a) Faulty Using the law of total probability: P[Faulty] = P[Faulty|Factory A]P[Line A] + P[Faulty|Line B]P[Line B] + P[Faulty|Line C]P[Line C] \[.02 \times .3 + .03 \times .25 + .05 \times .45\] .036 or 3.6% chance
anonymous
  • anonymous
I believe that b) can now be solved using Bayes' theorem. Let F = faulty and B = line B. Now Bayes' theorem is: \[P(B|F)=(P(B)P(F|B))/P(F)\] Plug in the values we allready have we get: \[P(B|F)=(0.25\times0.03)/0.036\] \[P(B|F)\approx0.21\]

Looking for something else?

Not the answer you are looking for? Search for more explanations.