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!

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


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    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)
    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

    User Avatar
    Science Advisor
    Homework Helper

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

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook