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.

 

[Architeuthis Dux]

I can provide some guidance on how to approach this problem. First, it is important to understand the given probability density function and what it represents. This function is used to calculate the probability of a battery lasting a certain number of hours, with the variable x representing the number of hours.

In order to find the probability that a battery will last at least another 50 hours after already lasting 180 hours, we need to find the area under the probability density function curve from 180 to 230 hours. This can be done by integrating the function from 180 to 230, which will give us the probability of the battery lasting between those two times.

The boundaries for the integration are the values of x, which in this case are the hours. So, the integral will be from 180 to 230. The result of the integration will give us the probability of the battery lasting between 180 and 230 hours. We can then use this probability to calculate the probability that the battery will last at least another 50 hours by subtracting the probability of it lasting less than 230 hours from the probability of it lasting less than 180 hours.

In summary, the approach to solving this problem involves integrating the probability density function from 180 to 230 hours, and then using the resulting probability to calculate the probability of the battery lasting at least another 50 hours. I hope this helps and good luck with your homework!