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Homework Help: Simple probability question that I want to have work checked

  1. Aug 31, 2015 #1
    1. The problem statement, all variables and given/known data
    A manufacturing machine produces defects with a probability of 0.1%. How many parts must the machine produce to have a 99.9% chance of producing at least 1 defective part?

    2. Relevant equations

    P(A) + P(B) = 1

    3. The attempt at a solution

    A in this case is the machine produces at least one defective part
    B is the case when the machine produces all good parts

    The probability that the machine produces a good part in the first try is:
    P(B) = 1 - .001 = .999

    The probability that the machine produces two good parts consecutively is:
    P(B) = .999*.999 = .999^2

    So I assume the probability that the machine produces n good parts consecutively would be:
    P(B) = .999^n

    Therefore the probability that the machine produces at least 1 bad part part within n consecutive parts must be:
    P(A) = 1 - .999^n

    Using P(A) = .999 and solving for n.

    .999 = 1 - .999^n

    ln(.001)/(ln(.999) = n = 6904.3 = 6905 parts

    Does that make sense? That we need to produce 6905 parts to have a 99.9 percent chance of 1 defective part?
    Last edited: Sep 1, 2015
  2. jcsd
  3. Sep 1, 2015 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    The probability that all of the first ##n## parts are good is ##P_n = 0.999^n##, so the complement of that is the probability that not all of the first ##n## parts are good. Your use of the word "after" threw me; I would rather use the word "among" or "within", because that is exactly what the quantity ##1-P_n## would mean.

    Anyway, you computations make sense and are also correct.

    PS: why do you write in all bold font? It makes it look like you are shouting!
  4. Sep 1, 2015 #3
    Oops sorry. I clicked the space after the 3rd question, and everything after that came out bold. I just realized now that there is a formatting tool above. I'll edit that.
  5. Sep 1, 2015 #4
    Thanks for taking a look. :smile:
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