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Homework Help: Conditional Probability problem

  1. Feb 8, 2012 #1
    1. The problem statement, all variables and given/known data
    A manufacturer of scientific workstations produces its new model at sites A, B, and C; 20% at A, 35% at B, and the remaining 45% at C. The probability of shipping a defective model is 0.01 if shipped from site A, 0.06 if from site B, and 0.03 if from site C.

    A- What is the probability that a randomly selected customer receives a defective model?
    B- If you receive a defective workstation, what is the probability that it was manufactured at site B?


    2. Relevant equations



    3. The attempt at a solution
    For A I got .0365 which was correct but I'm stuck on part B. My assumption was that I had to find P(B|DB) where DB is being from site B and defective so I would use the equation
    P(B^DB)/P(DB) I just don't know how I'm supposed to find P(B|DB) when I don't know what P(B^DB) is
     
  2. jcsd
  3. Feb 8, 2012 #2

    vela

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    You should just be calculating P(B|defective). The condition shouldn't specify where it came from. Think about it. If it's given that the workstation is defective and from site B, the probability it came from B is 1.
     
  4. Feb 8, 2012 #3
    I'm confused are you saying I should be calculating
    P(B|defective)= P(B^D)/P(D)=(.0365*.35)/(.0365)=.35 (which was counted wrong)
    OR
    that the probability is 1 which I don't get since the condition does specify that probability and there's not 100% chance it came from B since A & C have defective models also
     
    Last edited: Feb 8, 2012
  5. Feb 8, 2012 #4
    Never mind I figured it out. Thanks!
     
  6. Feb 8, 2012 #5

    Ray Vickson

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    [tex] P(B \cap D) = P(D \cap B) = P(D|B) P(B). [/tex]

    RGV
     
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