Question about probability and poisson process

[quacam09]

Hi all, I have a question about probability. Can you help me?

There are 2 events:
- Customer A arrives the system B in accordance with a Poisson process with rate Lambda1
- Customer A arrives the system C in accordance with a Poisson process with rate Lambda2.

Given that Poisson processes are mutually independent. Computing the probability of the event that customer A arrivers the system B and the probability of the event that customer A arrivers the system C?

Thank you!

 

[Focus]

I'm guessing there is only one custumer. The holding times are exponential with parameter lambda. The question then is $\mathbb{P}(\mathbf{e}_{\lambda_1}< \mathbf{e}_{\lambda_2})$. Condition on one of them and use the law of total probability.

 

[quacam09]

Thank you. As your suggestion, I found the solution.