Answer:
[tex]\frac{27}{175}[/tex]
Step-by-step explanation:
hello,
this question is drawn from queuing theory where the servers is the single repair person and the customer is the machine, thus we have 3 customers and a single server.
we shall obtain a Markov chain of the form M/M/1/3 queue where 1/3 and 1/4 are the arrival rate and service rate respectively.
the steady-state [tex]p_{3}[/tex] is given as ;
[tex][tex]p_{3} =\frac{\beta ^{3}(1-\beta )}{1-\beta ^{4} }[/tex] \\where\ \ \beta = \frac{3}{4}[/tex]
⇒[tex]p_{3}[/tex] = [tex][tex]\frac{\frac{27}{64}(1-\frac{3}{4})}{1-\frac{81}{256}}[/tex][/tex] = [tex]\frac{27}{175}[/tex]
