3. A production facility has two stages in tandem, with no waiting room in between. Scrvice times at the two stages follow independent exponential distributions with parameters (rates) 41 and 12. Jobs...

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Extracted text: 3. A production facility has two stages in tandem, with no waiting room in between. Scrvice times at the two stages follow independent exponential distributions with parameters (rates) 41 and 12. Jobs arrive at the facility following a Poisson process with rate X. An arriving job will be denied entry if upon arrival stage 1 is occupied. At time zero, there are two jobs in service at the two stages. Derive the probability that the next arriving job will find stage 1 vacant and hence be admitted.