The time $T$ required to repair a machine is an exponentially distributed random variable with mean 2.5 (hours). What is the probability that a repair takes at least $12 \frac{1}{2}$ hours given that its duration exceeds 12 hours?

Select the correct answer:

A. $1-e^{-2.5}$
B. $1-\frac{1}{2.5}e^{-\frac{1}{5}}$
C. $e^{-\frac{1}{5}}$
D. $e^{-2.5}$
E. $1-e^{-\frac{1}{5}}$