(Solved): The time \( T \) required to repair a machine is an exponentially distributed random variable with ...

The time \( T \) required to repair a machine is an exponentially distributed random variable with mean 4 (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. \( 1-e^{-\frac{1}{8}} \) B. \( 1-\frac{1}{4} e^{-\frac{1}{8}} \) C. \( e^{-\frac{1}{8}} \) D. \( 1-e^{-4} \) E. \( e^{-4} \)