Application for exponential distribution

[Askhwhelp]

The amount of time to finish a operation has an exponential distribution with mean 2 hours
Find the probability that the time to finish the operation is greater than 2 hours.

My thinking is to integrate the exponential probability function. After integrating it, I got -e^{-y/2} + 1 , 0 ≤ y < ∞

Then I use 1 - P(Y<=2) = 1 - (-e^{-2/2} +1) = e^-1

Is my approach correct? If so, could you check my answer please?

 

[Ray Vickson]

The amount of time to finish a operation has an exponential distribution with mean 2 hours
Find the probability that the time to finish the operation is greater than 2 hours.

My thinking is to integrate the exponential probability function. After integrating it, I got -e^{-y/2} + 1 , 0 ≤ y < ∞

Then I use 1 - P(Y<=2) = 1 - (-e^{-2/2} +1) = e^-1

Is my approach correct? If so, could you check my answer please?

Yes, it is correct.