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Probability: Is the manager telling the truth?

  1. Mar 5, 2014 #1
    1. The problem statement, all variables and given/known data

    The manager of a factory proclaims 99% of the products manufactured in his factory are unflawed. If we draw 50 products from 5000 products and find 2 of 50 are flawed, then how do we know the manage is telling the truth?

    2. Relevant equations

    Nothing special.

    3. The attempt at a solution

    Answer:

    [itex] \frac{{5000*0.99 \choose 48} {5000*0.01 \choose 2}}{ {5000 \choose 50}} \approx 0.0754 [/itex]

    Manager lied.

    Is this correct? Thank you in advance!
     
  2. jcsd
  3. Mar 5, 2014 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    You cannot conclude that the manager lied based on this result. You could have been unlucky with the 50 products. A probability of 7.5% is still reasonable and needs more tests before such a strong conclusion can be drawn.
     
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