3. A computer system is subject to failures and self-repairs. The failures occur according to a Poisson process at a rate of 2.5 per day. The self-repairs are instantaneous. The only effect of a failure is that the work done on any program running on the machine at the time of failure is lost and the program has to be restarted from scratch. Consider a program whose execution time is 4.5 hours if uninterrupted by failures. What is the probability that the program completes successfully without a restart?
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