How Do You Calculate Battery Life Probability After 180 Hours?

[EskShift]

Homework Statement

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?

Homework Equations

Integration

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? I am 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)

 

[statdad]

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.