A system consists of one component whose life time is exponentially distributed with mean
50 hours. When the component fails, it is immediately replaced by a spare component whose
lifetime is independent and identically distributed as that of original component without the
system suffering a down time. (A) What is the probability that the system has not failed after
100 hours of operation?

Question

A system consists of one component whose life time is exponentially distributed with mean
50 hours. When the component fails, it is immediately replaced by a spare component whose
lifetime is independent and identically distributed as that of original component without the
system suffering a down time. (A) What is the probability that the system has not failed after
100 hours of operation?

anonymous · Answer

A friend of mine asked me this question and I haven't been able to solve it.
P.S. he gave me the answer , i just don't know how to get to it.