Exponential with Poisson: post office has two clerks. After three people, A, B, and C, enter simultaneously, A and B go directly to the clerks....

[PennStater]

post office has two clerks. After three people, A, B, and C, enter simultaneously, A and
B go directly to the clerks and C waits until either A or B leaves before she begins service.
What is the probability that A is still in the post office after B and C have left when the
service times are independent and exponentially distributed with rate λ?

I can do the question with mean 1/mu, but I'm not sure where to start with rate

 

[Steven G]

Please show us your attempts even if you know it is wrong. We need to have some idea where you are stuck. Even if you tell us why you think that you can't do this it will be helpful.

 

[PennStater]

Yeah definitely. In the textbook it only shows with mean not a rate as seen in the above question.
Heres how far i go with the mean of 1/mu