1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Conditional probability and defect rate

  1. Sep 12, 2012 #1
    1. The problem statement, all variables and given/known data

    Of the items produced daily by a factory, 40% come from line I and 60% from line II. Line I
    has a defect rate of 8%, whereas line II has a defect rate of 10%. If an item is chosen at random
    from the day’s production, find the probability that it will not be defective.

    2. Relevant equations

    3. The attempt at a solution

    My answer is 0.82 because Line I with no defect is 0.32+Line II with no defect is 0.50.
    1-Both lines defected (0.18)=0.82.

    Is my approach correct?
  2. jcsd
  3. Sep 12, 2012 #2
    I'd like to know how your numbers came about. Try drawing a tree diagram and see if you can find the results then; it'll help simplify the process.
  4. Sep 12, 2012 #3
    I drew a table:
    Def No Def
    I 0.08 0.32 0.40
    II 0.10 0.50 0.60
    0.18 0.82 1

    It is a little bit off but you can see that elements add up to 1. and you can also see the number 0.82 - this is my answer.
  5. Sep 12, 2012 #4
    No no, I'm requesting that you write out how you got your numbers. I'll give a hint; question if your table is correct. If you have a .4 chance of it being in line 1, and a .6 chance of the item being in line 2, would you say that the chance of it being in line 1 AND defect is .08? Or would it be something else?
  6. Sep 12, 2012 #5
    I see what you mean. My mistake is that I did not consider to multiply the probabilities by corresponding values.

    Then, my question is. Some problems that I solved earlier were easily solved by using tables like this. How do I distinguish which method to use?
  7. Sep 12, 2012 #6
    That's the tricky part. A key component is how the question is asked, but nothing beats practice. Probability is one of those subjects where you just have to keep doing problems over and over to gain intuition. Best of luck!

  8. Sep 12, 2012 #7

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Table, trees, formulas, whatever---they all say the same thing, perhaps in disguised form. There is no single right way: do whatever makes you fee comfortable.

    Let's compute P(D) = prob item is defective.
    (1) Formula: P(D) = P(D|I)*P(I) + P(D|II)*P(II) = (.08)*(.60)+(.10)*(.40) = 0.0.088
    (2) Table: Say we make 1,000,000 items.
    No. produced in Line I = (0.60)(1,000,000) = 600,000
    No. produced in Line II = (0.40)(1,000,000) = 400,000
    Of the 600,000 produced on LI, the number defective = (.08)(600,000) = 48,000
    Of the 400,000 produced on LII the number defective = (.10)(400,000) = 40,000
    Putting these in a table we have:

    Total Defect Non-defect
    Line I items 600,000 48,000 552,000
    Line II items 400,000 40 000 360,000
    Total 1,000,000 88,000 912,000
    Thus, P(D) = 88,000/1,000,000 = 88/1000 = 0.088.

    You can also do it in a tree, but I can't easily draw a tree here.

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Conditional probability and defect rate
  1. Conditional probability (Replies: 11)

  2. Conditional Probability (Replies: 10)