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Very tough probability question, need some help!

  1. Sep 22, 2009 #1
    1. The problem statement, all variables and given/known data
    The life (in hours) of a particular brand of batteries is a random variable with probability density function given by f(x) = {1/1000e^(-x/1000)}, x ≥ 0, 0 elsewhere.

    If after 180 hours of operation a battery is still working, what is the probability that it will last at least another 50 hours?


    2. Relevant equations
    Integration


    3. The attempt at a solution
    Integration of the equation, which becomes [-e^(-x/1000)]
    Problem is, what boundaries is it supposed to have?
    I have figured out from 0 --> 180, that is a given right? Because the question states 'if after 180 hours of operation', so it must have worked up to 180 hours.
    but now what? im sure it has got to do with finding the Probability (B) | Probability (A), which is equal to Pr (A|B) = Pr (A intersect B) / Pr (B)
     
  2. jcsd
  3. Sep 22, 2009 #2

    statdad

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    Homework Helper

    This is a conditional probability question: given that it has lasted 180 hours (that's the event on which to condition) you need to know the probability it will last another 50 hours.
     
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