1. Exponential Distribution Conditional Probability

Hello, I have been working with Exponential Distribution problems, but have not come across a problem like this one with both Exponential Distribution and Conditional Probabilities:

If the lifetime of an electronic equipment follows an Exponential Distribution with parameter 0.1 hour. Given that it has already lasted for 10 hours, what is the conditional probability that it lasts for more than 25 hours?

I know the two formulas for if it will last up to a certain number of hours (1-e^(-0.1*x)) and if it will last more than a number of hours (e^(-0.1*x)). But I really cannot figure out how to find this conditional probability. Any help would be awesome! Thanks

2. Re: Exponential Distribution Conditional Probability

There is a small trick. The exponential distribution is memoryless. https://en.wikipedia.org/wiki/Memorylessness
Reset the problem to time zero at 10 hrs and use 15 hours.

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