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!

Uniform discrete probablity distributions

  1. Aug 22, 2014 #1
    1. The problem statement, all variables and given/known data
    An electric circuit has 5 components. It is known that one of the componenets is faulty. To detremine which one is faulty, all 5 componenets are tested one by one until the faulty component is found, The random variable X represents the number of test required to determine the faulty unit.


    2. Relevant equations



    3. The attempt at a solution
    here's my working:
    I let X = number of tests conducted until the faulty unit is found
    P(X= 1) = 1/5
    P(X=2) = P(good) x P( faulty ) = 4/5 x 1/5 = 0.16
    P(X=3) = P(good) x P(good) x P( faulty ) = 4/5 x 4/5 x 1/5 = 0.128
    P(X=4) = P(good) x P(good) x P(good) x P( faulty ) = 4/5 x 4/5 x 4/5 x 1/5 = 64/625
    P(X=5) = P(good) x P(good) x P(good) x P(good) x P( faulty ) = 4/5 x 4/5 x 4/5 x 4/5 x 1/5 = 256/3125


    But for the discrete probablity distributions , sum of all probability must be equal to 1 ... my sum of probability isn't equal to 1 , which is indeed wrong. why cant i do in this way?
     
  2. jcsd
  3. Aug 22, 2014 #2
    0.16 + 0.128+ 1/5 + 64/625 +256/3125 not equal to 1
     
  4. Aug 22, 2014 #3

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Because after observing the first one to be non-defective the remaining four are known to have one defective. That changes probabilities to 1/4 now.
     
    Last edited: Aug 22, 2014
  5. Aug 22, 2014 #4
    do you mean the P(x=2) should be 4/5 x 1/4 = 4/20 ?
     
  6. Aug 22, 2014 #5

    Orodruin

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Yes. What do you think this implies for the remaining probabilities?
     
  7. Aug 22, 2014 #6

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

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

Have something to add?
Draft saved Draft deleted



Similar Discussions: Uniform discrete probablity distributions
Loading...